Year: 2026
Type: preprint
Abstract: Let $M_n$ be an $n\times n$ matrix with independent uniform sign entries. We prove that there exist absolute constants $C,c>0$ such that, for all sufficiently large $n$, \[ \mathbb{P}\!\left( \left|\operatorname{Per}(M_n)\right| \ge e^{-Cn}\sqrt{n!} \right) \ge 1-n^{-c}. \] This establishes the exponential scale lower bound suggested by Tao and Vu. The proof bounds the cumulative logarithmic loss of the sum of squared permanents of minors under row exposure.
Source: arXiv (Cornell University)
Author: Chen, Yiming
Institution: Peking University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G8700735110
OpenAlex ID: W7204584942