ProbXiv
sign in
Problem archiveProblem record

Chafai-Dadoun-Youssef Questions on Logarithmic Energy Monotonicity

Probability & statistics · posed by Djalil Chafai, Benjamin Dadoun, Pierre Youssef · disproved

1 comment

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.

Record

Source
Added

Comments

No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Theodoros Assiotis, using ChatGPT Pro 5.5, ChatGPT 5.6 Sol Ultra

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The disclosure says the tools were used for ideation, technical help, editing and checking the proofs, and puts the contribution at the level of a co-author, while the author retains responsibility for mistakes. It does not separate which of the two counterexamples came from where.

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.