Chafai-Dadoun-Youssef Questions on Logarithmic Energy Monotonicity
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Statement
Chafai, Dadoun and Youssef asked whether the quadratically penalised logarithmic energy of mean empirical spectral distributions is monotone in the dimension, for Wigner matrices and for matrices with i.i.d. entries. Neither holds: a finite-energy Wigner counterexample and a one-parameter family of Gaussian-regularised Bernoulli entry laws answer both questions negatively.
Context
Two numbered questions from a recent random-matrix paper, documented but read within one community.
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