pith. sign in

arxiv: 2607.02233 · v1 · pith:YEPTN4H6new · submitted 2026-07-02 · ✦ hep-th · math.NT

Black Holes and Random Variables

Eric Perlmutter This is my paper

Pith reviewed 2026-07-03 08:36 UTC · model grok-4.3

classification ✦ hep-th math.NT
keywords AdS/CFTblack hole microstatesrandom matricesextreme value statisticsholographyconformal field theoryFyodorov-Hiary-Keating conjectureGaussian log-correlated fields
0
0 comments X

The pith

Black hole microstate counts follow the extreme value statistics of random matrices via an avatar of the Fyodorov-Hiary-Keating conjecture.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper formulates an avatar of the Fyodorov-Hiary-Keating conjecture for counting black hole microstates in quantum gravity. Through holography this produces sharp bounds on how many high-dimension primary operators appear in given intervals in the dual conformal field theory. The fluctuations in these counts are governed by a random variable whose tail distribution produces order-one erratic behavior at large N. A sympathetic reader would care because the result frames the resolution limit of the semiclassical AdS path integral as a statistical phenomenon inherited from random matrix universality classes.

Core claim

We formulate an avatar of the Fyodorov-Hiary-Keating conjecture for black hole microstate counts in quantum gravity. By holography, this implies sharp bounds on interval counts of high-dimension primary operators in conformal field theory. The extremal fluctuations of these counts are characterized by a random variable, with a prescribed tail distribution. At large N, these order-one erratic fluctuations set a quantitative limit on the resolution of the semiclassical AdS gravitational path integral. Gaussian random models for state counts arise naturally in this context; we express the phenomenon of erratic N-dependence in AdS/CFT as a decorrelation property of these models. Our broader poin

What carries the argument

The avatar of the Fyodorov-Hiary-Keating conjecture applied to black hole microstate counts, transferred by holography to interval counts of CFT primaries and characterized by a random variable with prescribed tail distribution.

If this is right

  • Sharp bounds appear on the number of high-dimension primary operators lying in specified intervals in CFT spectra.
  • Order-one erratic fluctuations at large N impose a quantitative limit on how finely the semiclassical AdS gravitational path integral can resolve microstate counts.
  • Erratic N-dependence in AdS/CFT is recast as a decorrelation property of Gaussian random models for state counts.
  • Microstate spectra and their CFT duals belong to the universality class of Gaussian log-correlated fields.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same statistical framework might be applied to other holographic dualities to predict fluctuation patterns in state counting.
  • Numerical checks of operator distributions in concrete large-N CFTs could provide a direct test of the tail behavior.
  • If the avatar holds, tools developed for extreme-value problems in random matrices could be imported to constrain quantum-gravity observables.

Load-bearing premise

The Fyodorov-Hiary-Keating conjecture admits a meaningful avatar formulation for black hole microstate counts in quantum gravity that can be transferred via holography to CFT operator counts.

What would settle it

A direct count or numerical sampling of black hole microstates or CFT operator intervals that fails to exhibit the predicted tail distribution of the random variable.

read the original abstract

We formulate an avatar of the Fyodorov-Hiary-Keating conjecture for black hole microstate counts in quantum gravity. By holography, this implies sharp bounds on interval counts of high-dimension primary operators in conformal field theory. The extremal fluctuations of these counts are characterized by a random variable, with a prescribed tail distribution. At large $N$, these order-one erratic fluctuations set a quantitative limit on the resolution of the semiclassical AdS gravitational path integral. Gaussian random models for state counts arise naturally in this context; we express the phenomenon of erratic $N$-dependence in AdS/CFT as a decorrelation property of these models. Our broader point is to suggest that AdS black hole microstate spectra and their field theory duals should exhibit the extreme value statistics of random matrices, lying in the universality class of Gaussian log-correlated fields.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript formulates an avatar of the Fyodorov-Hiary-Keating conjecture for the statistics of black hole microstate counts in AdS quantum gravity. Via holography this implies that counts of high-dimension primary operators in the dual CFT exhibit the extreme-value statistics of Gaussian log-correlated random fields, producing order-one erratic fluctuations at large N that quantitatively limit the resolution of the semiclassical gravitational path integral; the authors recast the phenomenon of erratic N-dependence as a decorrelation property of Gaussian random models for state counts.

Significance. If the proposed avatar can be made precise and tested, the work would establish a concrete link between extreme-value statistics from number theory and the microstate spectra of AdS black holes, supplying falsifiable predictions for fluctuations in CFT operator counts and a new diagnostic for the breakdown of semiclassical approximations. The explicit framing as a conjecture rather than a derivation is a strength that keeps the contribution proportionate to its scope.

minor comments (2)
  1. [Abstract] Abstract: the phrase 'a random variable, with a prescribed tail distribution' is introduced without naming the distribution or the random variable; the main text should supply the explicit form of the avatar (including how the FHK tail is transferred to microstate interval counts) so that the conjecture is stated with sufficient precision for future work.
  2. The manuscript correctly identifies all steps as conjectural, but a short dedicated subsection outlining the minimal assumptions required for the holography transfer (e.g., how microstate counting maps to CFT primary counting) would improve readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive evaluation, accurate summary of the manuscript, and recommendation of minor revision. The significance assessment aligns with our intent to frame the work as a conjecture linking extreme-value statistics to AdS/CFT spectra.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper explicitly frames its main contribution as formulating an 'avatar' of the external Fyodorov-Hiary-Keating conjecture for black hole microstate counts, with the transfer to CFT operator counts via holography also presented as conjectural. No derivation chain is claimed from first principles; the text does not fit parameters to data within the paper and then relabel them as predictions, nor does it rely on self-citations for load-bearing uniqueness theorems or ansatze. The central claim is the proposal itself, which remains independent of any internal reduction and is benchmarked against an external number-theoretic conjecture.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on adapting an external number theory conjecture to quantum gravity without new derivations or independent evidence supplied in the abstract.

axioms (1)
  • domain assumption The Fyodorov-Hiary-Keating conjecture admits a direct avatar formulation for black hole microstate counts
    Invoked as the starting point for the proposed connection to quantum gravity.
invented entities (1)
  • Random variable characterizing extremal fluctuations of microstate interval counts no independent evidence
    purpose: To prescribe the tail distribution of high-dimension primary operator counts in CFT
    Introduced in the abstract to describe the erratic fluctuations at large N

pith-pipeline@v0.9.1-grok · 5660 in / 1320 out tokens · 36625 ms · 2026-07-03T08:36:29.488336+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

86 extracted references · 72 canonical work pages · 39 internal anchors

  1. [1]

    Y. V. Fyodorov, G. A. Hiary, and J. P. Keating,Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function,Physical Review Letters108(2012), no. 17 170601, [arXiv:1202.4713]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  2. [2]

    Y. V. Fyodorov and J. P. Keating,Freezing Transitions and Extreme Values: Random Matrix Theory,ζ(1/2 +it), and Disordered Landscapes,Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences372(2014), no. 2007 20120503, [arXiv:1211.6063]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  3. [3]

    H. L. Montgomery,The Pair Correlation of Zeros of the Zeta Function,Proceedings of the American Mathematical Society24(1973), no. 3 519–522

    1973

  4. [4]

    A. M. Odlyzko,On the Distribution of Spacings Between Zeros of the Zeta Function, Mathematics of Computation48(1987), no. 177 273–308

    1987

  5. [5]

    J. L. Cardy,Operator Content of Two-Dimensional Conformally Invariant Theories, Nucl. Phys. B270(1986) 186–204

    1986

  6. [6]

    Large rotating AdS black holes from fluid mechanics

    S. Bhattacharyya, S. Lahiri, R. Loganayagam, and S. Minwalla,Large Rotating AdS Black Holes from Fluid Mechanics,Journal of High Energy Physics2008(2008), no. 9 054, [arXiv:0708.1770]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  7. [7]

    Black hole microstates in AdS

    E. Shaghoulian,Black Hole Microstates in AdS,Physical Review D94(2016), no. 10 104044, [arXiv:1512.06855]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  8. [8]

    Benjamin, J

    N. Benjamin, J. Lee, H. Ooguri, and D. Simmons-Duffin,Universal Asymptotics for High Energy CFT Data,Journal of High Energy Physics2024(2024), no. 3 115, [arXiv:2306.08031]. 30

    work page arXiv 2024

  9. [9]

    Maximum of the characteristic polynomial of random unitary matrices

    L.-P. Arguin, D. Belius, and P. Bourgade,Maximum of the Characteristic Polynomial of Random Unitary Matrices,Communications in Mathematical Physics349(2017), no. 2 703–751, [arXiv:1511.07399]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  10. [10]

    The maximum of the CUE field

    E. Paquette and O. Zeitouni,The Maximum of the CUE Field,International Mathematics Research Notices2018(2018), no. 16 5028–5119, [arXiv:1602.08875]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  11. [11]

    On the maximum of the C$\beta$E field

    R. Chhaibi, T. Madaule, and J. Najnudel,On the Maximum of theCβEField,Duke Mathematical Journal167(2018), no. 12 2243–2345, [arXiv:1607.00243]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  12. [12]

    Y. V. Fyodorov and P. Le Doussal,Statistics of Extremes in Eigenvalue-Counting Staircases,Physical Review Letters124(2020) 210602, [arXiv:2001.04135]

    work page arXiv 2020

  13. [13]

    J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher, and M. Tezuka,Black Holes and Random Matrices,JHEP05(2017) 118, [arXiv:1611.04650]. [Erratum: JHEP 09, 002 (2018)]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  14. [14]

    The maximum deviation of the Sine$_\beta$ counting process

    D. Holcomb and E. Paquette,The Maximum Deviation of the SineβCounting Process, Electronic Communications in Probability23(2018) Paper No. 58, 13 pp., [arXiv:1801.08989]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  15. [15]

    How much can the eigenvalues of a random Hermitian matrix fluctuate?

    T. Claeys, B. Fahs, G. Lambert, and C. Webb,How Much Can the Eigenvalues of a Random Hermitian Matrix Fluctuate?,Duke Mathematical Journal170(2021), no. 9 2085–2235, [arXiv:1906.01561]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  16. [16]

    Bourgade, P

    P. Bourgade, P. Lopatto, and O. Zeitouni,Optimal Rigidity and Maximum of the Characteristic Polynomial of Wigner Matrices,Geometric and Functional Analysis35 (2025), no. 1 161–253, [arXiv:2312.13335]

    work page arXiv 2025

  17. [17]

    OPE Convergence in Conformal Field Theory

    D. Pappadopulo, S. Rychkov, J. Espin, and R. Rattazzi,OPE Convergence in Conformal Field Theory,Physical Review D86(2012) 105043, [arXiv:1208.6449]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  18. [18]

    Remarks on the Convergence Properties of the Conformal Block Expansion

    S. Rychkov and P. Yvernay,Remarks on the Convergence Properties of the Conformal Block Expansion,Physics Letters B753(2016) 682–686, [arXiv:1510.08486]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  19. [19]

    A tauberian theorem for the conformal bootstrap

    J. Qiao and S. Rychkov,A Tauberian Theorem for the Conformal Bootstrap,Journal of High Energy Physics2018(2018), no. 4 093, [arXiv:1709.00008]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  20. [20]

    Mukhametzhanov and A

    B. Mukhametzhanov and A. Zhiboedov,Analytic Euclidean Bootstrap,Journal of High Energy Physics2019(2019), no. 10 270, [arXiv:1808.03212]

    work page arXiv 2019

  21. [21]

    Mukhametzhanov and A

    B. Mukhametzhanov and A. Zhiboedov,Modular Invariance, Tauberian Theorems and Microcanonical Entropy,JHEP10(2019) 261, [arXiv:1904.06359]

    work page arXiv 2019

  22. [22]

    Mukhametzhanov and S

    B. Mukhametzhanov and S. Pal,Beurling-Selberg Extremization and Modular Bootstrap at High Energies,SciPost Phys.8(2020), no. 6 088, [arXiv:2003.14316]

    work page arXiv 2020

  23. [23]

    B. C. van Rees,Theorems for the lightcone bootstrap,SciPost Phys.18(2025), no. 6 207, [arXiv:2412.06907]. 31

    work page arXiv 2025

  24. [24]

    Y. V. Fyodorov and J.-P. Bouchaud,Freezing and Extreme-Value Statistics in a Random Energy Model with Logarithmically Correlated Potential,Journal of Physics A: Mathematical and Theoretical41(2008), no. 37 372001, [arXiv:0805.0407]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  25. [25]

    E. C. Bailey and J. P. Keating,Maxima of Log-Correlated Fields: Some Recent Developments,Journal of Physics A: Mathematical and Theoretical55(2022), no. 5 053001, [arXiv:2106.15141]

    work page arXiv 2022

  26. [26]

    J. P. Keating and N. C. Snaith,Random Matrix Theory andζ(1/2 +it), Communications in Mathematical Physics214(2000) 57–89

    2000

  27. [27]

    S. S. Gubser, I. R. Klebanov, and A. W. Peet,Entropy and Temperature of Black 3-Branes,Physical Review D54(1996) 3915–3919, [hep-th/9602135]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  28. [28]

    Extrema of log-correlated random variables: Principles and Examples

    L.-P. Arguin,Extrema of Log-Correlated Random Variables: Principles and Examples, inAdvances in Disordered Systems, Random Processes and Some Applications (P. Contucci and C. Giardinà, eds.), pp. 166–204. Cambridge University Press, 2017. arXiv:1601.00582

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  29. [29]

    M. D. Bramson,Maximal Displacement of Branching Brownian Motion, Communications on Pure and Applied Mathematics31(1978), no. 5 531–581

    1978

  30. [30]

    Dembo and O

    A. Dembo and O. Zeitouni,Large Deviations Techniques and Applications, vol. 38 of Applications of Mathematics. Springer, New York, second ed., 1998

    1998

  31. [31]

    Subag and O

    E. Subag and O. Zeitouni,Freezing and decorated Poisson point processes, Communications in Mathematical Physics337(2015), no. 1 55–92

    2015

  32. [32]

    Paquette and O

    E. Paquette and O. Zeitouni,The Extremal Landscape for theCβEEnsemble,Forum of Mathematics, Sigma13(2025) e1, [arXiv:2209.06743]

    work page arXiv 2025

  33. [33]

    D. W. Farmer, S. M. Gonek, and C. P. Hughes,The Maximum Size ofL-Functions, Journal für die reine und angewandte Mathematik609(2007) 215–236, [math/0506218]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  34. [34]

    Soundararajan,The Distribution of Values of Zeta andL-Functions, inProceedings of the International Congress of Mathematicians 2022, vol

    K. Soundararajan,The Distribution of Values of Zeta andL-Functions, inProceedings of the International Congress of Mathematicians 2022, vol. 2, pp. 1260–1310. EMS Press, 2022

    2022

  35. [35]

    Mesoscopic fluctuations of the zeta zeros

    P. Bourgade,Mesoscopic Fluctuations of the Zeta Zeros,Probability Theory and Related Fields148(2010), no. 3–4 479–500, [arXiv:0902.1757]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  36. [36]

    Y. V. Fyodorov and N. J. Simm,On the Distribution of the Maximum Value of the Characteristic Polynomial of GUE Random Matrices,Nonlinearity29(2016), no. 9 2837–2855, [arXiv:1503.07110]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  37. [37]

    Lambert and E

    G. Lambert and E. Paquette,The law of large numbers for the maximum of almost gaussian log-correlated fields coming from random matrices,Probability Theory and Related Fields173(2019), no. 1 157–209

    2019

  38. [38]

    Lambert and E

    G. Lambert and E. Paquette,Strong Approximation of Gaussianβ-Ensemble Characteristic Polynomials: The Hyperbolic Regime,The Annals of Applied Probability 33(2023), no. 1 107–156, [arXiv:2001.09042]. 32

    work page arXiv 2023

  39. [39]

    Lambert and E

    G. Lambert and E. Paquette,Strong Approximation of Gaussianβ-Ensemble Characteristic Polynomials: The Edge Regime and the Stochastic Airy Function, Random Matrices: Theory and Applications13(2024), no. 2 2450014, [arXiv:2009.05003]

    work page arXiv 2024

  40. [40]

    E. C. Bailey and J. P. Keating,On the Moments of the Moments of the Characteristic Polynomials of Random Unitary Matrices,Communications in Mathematical Physics 371(2019) 689–726, [arXiv:1807.06605]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  41. [41]

    Assiotis and J

    T. Assiotis and J. P. Keating,Moments of Moments of Characteristic Polynomials of Random Unitary Matrices and Lattice Point Counts,International Mathematics Research Notices2020(2020), no. 23 9189–9202, [arXiv:1905.06072]

    work page arXiv 2020

  42. [42]

    The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos - The $L^2$-phase

    C. Webb,The Characteristic Polynomial of a Random Unitary Matrix and Gaussian Multiplicative Chaos: TheL2-Phase,Electronic Journal of Probability20(2015) Paper No. 104, 21 pp., [arXiv:1410.0939]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  43. [43]

    Multiplicative chaos and the characteristic polynomial of the CUE: the $L^1$-phase

    M. Nikula, E. Saksman, and C. Webb,Multiplicative Chaos and the Characteristic Polynomial of the CUE: TheL1-Phase,Transactions of the American Mathematical Society373(2020), no. 6 3905–3965, [arXiv:1806.01831]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  44. [44]

    Lambert and J

    G. Lambert and J. Najnudel,Subcritical Multiplicative Chaos and the Characteristic Polynomial of theCβE,Probability Theory and Related Fields(2026) [arXiv:2407.19817]

    work page arXiv 2026

  45. [45]

    Maximum of the Riemann zeta function on a short interval of the critical line

    L.-P. Arguin, D. Belius, P. Bourgade, M. Radziwiłł, and K. Soundararajan,Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line,Communications on Pure and Applied Mathematics72(2019), no. 3 500–535, [arXiv:1612.08575]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  46. [46]

    On the extreme values of the Riemann zeta function on random intervals of the critical line

    J. Najnudel,On the Extreme Values of the Riemann Zeta Function on Random Intervals of the Critical Line,Probability Theory and Related Fields172(2018), no. 1–2 387–452, [arXiv:1611.05562]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  47. [47]

    A. J. Harper,On the Partition Function of the Riemann Zeta Function, and the Fyodorov–Hiary–Keating Conjecture,arXiv:1906.05783

    work page internal anchor Pith review Pith/arXiv arXiv 1906

  48. [48]

    A. J. Harper,A Note on the Maximum of the Riemann Zeta Function, and Log-Correlated Random Variables,arXiv:1304.0677

    work page internal anchor Pith review Pith/arXiv arXiv

  49. [49]

    Maxima of a randomized Riemann zeta function, and branching random walks

    L.-P. Arguin, D. Belius, and A. J. Harper,Maxima of a Randomized Riemann Zeta Function, and Branching Random Walks,The Annals of Applied Probability27(2017), no. 1 178–215, [arXiv:1506.00629]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  50. [50]

    Arguin, P

    L.-P. Arguin, P. Bourgade, and M. Radziwiłł,The Fyodorov–Hiary–Keating Conjecture. I,arXiv preprint(2020) [arXiv:2007.00988]

    work page arXiv 2020

  51. [51]

    Arguin, P

    L.-P. Arguin, P. Bourgade, and M. Radziwiłł,The Fyodorov–Hiary–Keating Conjecture. II,arXiv preprint(2023) [arXiv:2307.00982]

    work page arXiv 2023

  52. [52]

    Arguin, F

    L.-P. Arguin, F. Ouimet, and M. Radziwiłł,Moments of the Riemann Zeta Function on Short Intervals of the Critical Line,The Annals of Probability49(2021), no. 6 3106–3141, [arXiv:1901.04061]. 33

    work page arXiv 2021

  53. [53]

    The Fyodorov--Hiary--Keating Conjecture on Mesoscopic Intervals

    L.-P. Arguin and J. Hamdan,The Fyodorov–Hiary–Keating Conjecture on Mesoscopic Intervals,arXiv preprint(2024) [arXiv:2405.06474]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  54. [54]

    Iwaniec and E

    H. Iwaniec and E. Kowalski,Analytic Number Theory, vol. 53 ofColloquium Publications. American Mathematical Society, 2004

    2004

  55. [55]

    Haake,Quantum Signatures of Chaos

    F. Haake,Quantum Signatures of Chaos. Physics and astronomy online library. Springer, 2001

    2001

  56. [56]

    G. B. Arous and P. Bourgade,Extreme gaps between eigenvalues of random matrices, The Annals of Probability41(2013), no. 4 2648 – 2681. [arXiv:1010.1294]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  57. [57]

    Small gaps in the spectrum of the rectangular billiard

    V. Blomer, J. Bourgain, M. Radziwiłł, and Z. Rudnick,Small gaps in the spectrum of the rectangular billiard,arXiv:1604.02413

    work page internal anchor Pith review Pith/arXiv arXiv

  58. [58]

    Katz and P

    N. Katz and P. Sarnak,Zeros of zeta functions and symmetry,BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume36(02, 1999) 1–26

    1999

  59. [59]

    Fast Scramblers

    Y. Sekino and L. Susskind,Fast Scramblers,Journal of High Energy Physics2008 (2008), no. 10 065, [arXiv:0808.2096]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  60. [60]

    A bound on chaos

    J. Maldacena, S. H. Shenker, and D. Stanford,A Bound on Chaos,Journal of High Energy Physics2016(2016), no. 8 106, [arXiv:1503.01409]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  61. [61]

    Comments on the Sachdev-Ye-Kitaev model

    J. Maldacena and D. Stanford,Remarks on the Sachdev–Ye–Kitaev Model,Physical Review D94(2016), no. 10 106002, [arXiv:1604.07818]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  62. [62]

    P. Saad, S. H. Shenker, and D. Stanford,A Semiclassical Ramp in SYK and in Gravity, arXiv:1806.06840

    work page internal anchor Pith review Pith/arXiv arXiv

  63. [63]

    AdS 3/RMT2 duality,

    G. Di Ubaldo and E. Perlmutter,AdS3/RMT2 Duality,JHEP12(2023) 179, [arXiv:2307.03707]

    work page arXiv 2023

  64. [64]

    Belin, J

    A. Belin, J. de Boer, P. Nayak, and J. Sonner,Generalized spectral form factors and the statistics of heavy operators,JHEP11(2022) 145, [arXiv:2111.06373]

    work page arXiv 2022

  65. [65]

    Random statistics of OPE coefficients and Euclidean wormholes,

    A. Belin and J. de Boer,Random statistics of OPE coefficients and Euclidean wormholes,Class. Quant. Grav.38(2021), no. 16 164001, [arXiv:2006.05499]

    work page arXiv 2021

  66. [66]

    Yan,More on torus wormholes in 3d gravity,JHEP11(2023) 039, [arXiv:2305.10494]

    C. Yan,More on torus wormholes in 3d gravity,JHEP11(2023) 039, [arXiv:2305.10494]

    work page arXiv 2023

  67. [67]

    Perlmutter,The Spectral Edge at Large Central Charge and Black Hole Statistics (to appear)

    E. Perlmutter,The Spectral Edge at Large Central Charge and Black Hole Statistics (to appear)

  68. [68]

    P. Saad, S. H. Shenker, D. Stanford, and S. Yao,Wormholes without averaging,JHEP 09(2024) 133, [arXiv:2103.16754]

    work page arXiv 2024

  69. [69]

    Quantum Gravity Partition Functions in Three Dimensions

    A. Maloney and E. Witten,Quantum Gravity Partition Functions in Three Dimensions, JHEP02(2010) 029, [arXiv:0712.0155]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  70. [70]

    AdS 3 gravity and random CFT,

    J. Cotler and K. Jensen,AdS3 Gravity and Random CFT,JHEP04(2021) 033, [arXiv:2006.08648]. 34

    work page arXiv 2021

  71. [71]

    Maxfield and G

    H. Maxfield and G. J. Turiaci,The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral,JHEP01(2021) 118, [arXiv:2006.11317]

    work page arXiv 2021

  72. [72]

    Surgery and statistics in 3d gravity

    J. de Boer, J. Kames-King, and B. Post,Surgery and statistics in 3d gravity, arXiv:2506.04151

    work page internal anchor Pith review Pith/arXiv arXiv

  73. [73]

    Approximate CFTs and random tensor models,

    A. Belin, J. de Boer, D. L. Jafferis, P. Nayak, and J. Sonner,Approximate CFTs and Random Tensor Models,JHEP09(2024) 163, [arXiv:2308.03829]

    work page arXiv 2024

  74. [74]

    D. L. Jafferis, L. Rozenberg, and G. Wong,3d gravity as a random ensemble,JHEP02 (2025) 208, [arXiv:2407.02649]

    work page arXiv 2025

  75. [75]

    Solving 3d gravity with Virasoro TQFT,

    S. Collier, L. Eberhardt, and M. Zhang,Solving 3D Gravity with Virasoro TQFT, SciPost Phys.15(2023) 151, [arXiv:2304.13650]

    work page arXiv 2023

  76. [76]

    P. Saad, S. H. Shenker, and D. Stanford,JT Gravity as a Matrix Integral, arXiv:1903.11115

    work page internal anchor Pith review Pith/arXiv arXiv 1903

  77. [77]

    Blommaert, T

    A. Blommaert, T. G. Mertens, and H. Verschelde,Eigenbranes in Jackiw-Teitelboim gravity,JHEP02(2021) 168, [arXiv:1911.11603]

    work page arXiv 2021

  78. [78]

    Altland, B

    A. Altland, B. Post, J. Sonner, J. van der Heijden, and E. Verlinde,Quantum Chaos in 2D Gravity,SciPost Physics15(2023) 064, [arXiv:2204.07583]

    work page arXiv 2023

  79. [79]

    Schlenker and E

    J.-M. Schlenker and E. Witten,No ensemble averaging below the black hole threshold, JHEP07(2022) 143, [arXiv:2202.01372]

    work page arXiv 2022

  80. [80]

    Liu,Towards a Holographic Description of Closed Universes,arXiv:2509.14327

    H. Liu,Towards a Holographic Description of Closed Universes,arXiv:2509.14327

    work page arXiv

Showing first 80 references.