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arXiv · 2607.24170

On non-monotonicity of logarithmic energy for random matrices

Theodoros Assiotis
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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 Chafa\"i, Dadoun, and Youssef.

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Theodoros Assiotis. 2026-07-27. On non-monotonicity of logarithmic energy for random matrices. https://arxiv.org/abs/2607.24170

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