Spectral gap for unlabelled Ginibre Interacting Brownian motion

Kohei Suzuki

arXiv:2608.17437v1 Primary: math.PR Secondary: math-ph, math.FA

Abstract

We determine the exact spectral gaps for both the finite-particle and infinite-particle unlabelled Ginibre interacting Brownian motions. In every finite-particle system, the spectral gap is equal to one, whereas for the infinite-particle system it is equal to two. The infinite-particle dynamics therefore has a strictly larger spectral gap than any of its finite-particle counterparts, revealing an enhancement of spectral gaps in the passage from finite to infinite particle systems.

Disclosure

“pectral gap is at most 2. Together with (3.14), this proves that the sharp spectral gap is exactly 2. ■ Disclosure. Interactive discussions with an AI tool assisted in exploring proof ideas and polishing the language. All mathematical details were independently verified by the author, who takes full responsibility for their correctness. Ref”
PDF page 13

Classification: Proof ideas or individual proof-step assistance
Multiplier: 8
Verified: 2026-08-23T05:21:30.002399Z

Structural counts

Pages 14 pdf

Theorems 2 source

Lemmas 3 source

Propositions 0 source

Corollaries 0 source

Definitions 0 source

Displayed equations 135 source

Bibliography entries 10 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file Ginibre_arXiv.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.