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A simple observation on random matrices with continuous diagonal entries

   
@article{ECP2633,
	author = {Omer Friedland and Ohad Giladi},
	title = {A simple observation on random matrices with continuous diagonal entries},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {18},
	year = {2013},
	keywords = {},
	abstract = {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$$$\mathbb{P}\Big[|\det(A+T)|^{1/n}\le t\Big]\le2bnt, $$where $b>0$ is a uniform upper bound on the densities of $T_{i, i}$.},
	pages = {no. 53, 1-7},
	issn = {1083-589X},
	doi = {10.1214/ECP.v18-2633},    
        url = {http://ecp.ejpecp.org/article/view/2633}}