Chafai-Dadoun-Youssef Questions on Logarithmic Energy Monotonicity

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probability-statisticsJul 27, 2026Significance 10/100Registry: unreviewed

Chafai-Dadoun-Youssef Questions on Logarithmic Energy Monotonicity

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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.

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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.

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