Chafai-Dadoun-Youssef Questions on Logarithmic Energy Monotonicity
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.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Random matrix theory
- Posed by
- Djalil Chafai, Benjamin Dadoun, Pierre Youssef
- Year posed
- 2024
- Years open
- 2y
- Solved
- 2026-07-27
- Model
- ChatGPT Pro 5.5, ChatGPT 5.6 Sol Ultra
- Vendor
- OpenAI
- Collaborators
- Theodoros Assiotis
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
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.
Verification
Single-author arXiv preprint; not yet peer-reviewed.