Pith. sign in

REVIEW 1 cited by

Joint probability densities of level spacing ratios in random matrices

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1305.7156 v1 pith:ZN2KBYTM submitted 2013-05-30 quant-ph cond-mat.stat-mechmath-phmath.MP

Y. Y. Atas , E. Bogomolny , O. Giraud , P. Vivo , E. Vivo This is my paper · ORCID
classification quant-phcond-mat.stat-mechmath-phmath.MP
keywords ratioslevelmatricesrandomcasesdensitiesensemblesjoint
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We calculate analytically, for finite-size matrices, joint probability densities of ratios of level spacings in ensembles of random matrices characterized by their associated confining potential. We focus on the ratios of two spacings between three consecutive real eigenvalues, as well as certain generalizations such as the overlapping ratios. The resulting formulas are further analyzed in detail in two specific cases: the beta-Hermite and the beta-Laguerre cases, for which we offer explicit calculations for small N. The analytical results are in excellent agreement with numerical simulations of usual random matrix ensembles, and with the level statistics of a quantum many-body lattice model and zeros of the Riemann zeta function.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. How Random Are Ergodic Eigenstates of the Ultrametric Random Matrices and the Quantum Sun Model?

    quant-ph 2025-01 conditional novelty 5.0 of 10

    Extreme value statistics of Schmidt eigenvalues reveal deviations from Wishart behavior in ergodic eigenstates of ultrametric random matrices and the Quantum Sun model.

Pith tools