PreprintCC BY 4.0arXiv
On non-monotonicity of logarithmic energy for random matrices
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.
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BibTeX
@misc{assiotis2026nonmonotonicity,
title = {{On non-monotonicity of logarithmic energy for random matrices}},
author = {Theodoros Assiotis},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.24170},
eprint = {2607.24170},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.24170},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On non-monotonicity of logarithmic energy for random matrices
AU - Theodoros Assiotis
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2607.24170
UR - https://arxiv.org/abs/2607.24170
AB - 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.
ER -