On non-monotonicity of logarithmic energy for random matrices

Theodoros Assiotis

arXiv:2607.24170v1 Primary: math.PR Secondary: math-ph

Abstract

We construct a finite-energy Wigner counterexample and a concrete one-parameter family of Gaussian-regularised Bernoulli entry laws yielding counterexamples to the conjectural dimensional monotonicity of the quadratically penalised logarithmic energy for mean empirical spectral distributions by Chafaï, Dadoun, and Youssef.

Disclosure

“≥ 1, ε > 0, and there exists ε0 > 0 such that FC (ν3,ε ) > FC (ν2,ε ), 0 < ε < ε0 . Tool and computational resource disclosure In the course of the research presented here I have been using AI tools, most significantly ChatGPT Pro 5.5 and ChatGPT 5.6 Sol Ultra for ideation, technical help, editing and checking the proofs and general editing and proofreading of the manuscript, at the level of a co-author. All mistakes are my own respon”
PDF page 3

Classification: Proof ideas or individual proof-step assistance
Multiplier: 8
Verified: 2026-08-23T19:08:16.445798Z

Structural counts

Pages 22 pdf

Theorems 2 source

Lemmas 9 source

Propositions 2 source

Corollaries 0 source

Definitions 0 source

Displayed equations 177 source

Bibliography entries 13 source

Appendix pages 0 estimated

Count notes

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