%0 Journal Article
%T A simple observation on random matrices with continuous diagonal entries
%A Omer Friedland
%A Ohad Giladi
%J Mathematics
%D 2013
%I arXiv
%X Let $T$ be an $n\times n$ random matrix, such that each diagonal entry $T_{i,i}$ is a continuous random variable, independent from all the other entries of $T$. Then for every $n\times n$ matrix $A$ and every $t\ge0$ $$ \p\Big[|\det(A+T)|^{1/n}\le t\Big]\le2bnt, $$ where $b>0$ is a uniform upper bound on the densities of $T_{i,i}$.
%U http://arxiv.org/abs/1302.0388v2