Pith Number

pith:G6LV7FCT

pith:2026:G6LV7FCTZ3KOCNAA4W4LHPPJNH

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Determinantal point processes associated with the Bochner-Schr\"odinger operator

Yuri A. Kordyukov

The determinantal point process tied to the spectral projection of the scaled Bochner-Schrödinger operator has linear statistics admitting explicit asymptotics as p tends to infinity.

arxiv:2605.13575 v1 · 2026-05-13 · math.DG · math-ph · math.MP · math.PR · math.SP

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Claims

C1strongest claim

We study the determinantal point process on X associated with the spectral projection of H_p corresponding to an interval I=(α,β) such that α,β∉Σ and compute the asymptotics of its linear statistics as p goes to infinity. When X is compact, this implies the law of large numbers and central limit theorem for the corresponding empirical measures.

C2weakest assumption

The non-degeneracy of the curvature form of L together with the bounded-geometry assumption on the Riemannian manifold X; these are invoked to guarantee that the local Landau levels remain separated and that the spectrum of H_p asymptotically coincides with their union Σ.

C3one line summary

Asymptotics of linear statistics for determinantal point processes from spectral projections of the Bochner-Schrödinger operator H_p are computed in the large-p limit, implying LLN and CLT on compact manifolds.

References

31 extracted · 31 resolved · 0 Pith anchors

[1] L. D. Abreu, Entanglement entropy and hyperuniformity of Ginibre and Weyl- Heisenberg ensembles.Lett. Math. Phys.113(2023), no. 3, Paper No. 54, 14 pp 2023

[2] L. D. Abreu, J. M. Pereira, J. L. Romero, and S. Torquato, The Weyl-Heisenberg ensemble: hyperuniformity and higher Landau levels.J. Stat. Mech. Theory Exp. 2017, no. 4, Paper No. 043103, 16 pp 2017

[3] G. W. Anderson, A. Guionnet, and O. Zeitouni,An introduction to random matrices, Cambridge Studies in Advanced Mathematics, vol. 118, Cambridge University Press, Cambridge, 2010 2010

[4] Berman, Determinantal point processes and fermions on complex manifolds: large deviations and bosonization.Comm 2014

[5] Berman, Determinantal point processes and fermions on polarized complex man- ifolds: bulk universality, InAlgebraic and analytic microlocal analysis,Springer Proc 2018

Formal links

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Receipt and verification

First computed	2026-05-18T02:44:23.300546Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37975f9453ced4e13400e5b8b3bde969c114e42fb5497fb3dd76ca65c9ec69c8

Aliases

arxiv: 2605.13575 · arxiv_version: 2605.13575v1 · doi: 10.48550/arxiv.2605.13575 · pith_short_12: G6LV7FCTZ3KO · pith_short_16: G6LV7FCTZ3KOCNAA · pith_short_8: G6LV7FCT

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/G6LV7FCTZ3KOCNAA4W4LHPPJNH \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 37975f9453ced4e13400e5b8b3bde969c114e42fb5497fb3dd76ca65c9ec69c8

Canonical record JSON

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      "math.PR",
      "math.SP"
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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-13T14:10:23Z",
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