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2013 A simple observation on random matrices with continuous diagonal entries
Omer Friedland, Ohad Giladi
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Electron. Commun. Probab. 18: 1-7 (2013). DOI: 10.1214/ECP.v18-2633

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 $T_{i, i}$.

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Omer Friedland. Ohad Giladi. "A simple observation on random matrices with continuous diagonal entries." Electron. Commun. Probab. 18 1 - 7, 2013. https://doi.org/10.1214/ECP.v18-2633

Information

Accepted: 30 June 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1300.60019
MathSciNet: MR3078016
Digital Object Identifier: 10.1214/ECP.v18-2633

Subjects:
Primary: 60B20
Secondary: 15B52

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