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May 2014 Random doubly stochastic matrices: The circular law
Hoi H. Nguyen
Ann. Probab. 42(3): 1161-1196 (May 2014). DOI: 10.1214/13-AOP877

Abstract

Let $X$ be a matrix sampled uniformly from the set of doubly stochastic matrices of size $n\times n$. We show that the empirical spectral distribution of the normalized matrix $\sqrt{n}(X-{\mathbf{E} }X)$ converges almost surely to the circular law. This confirms a conjecture of Chatterjee, Diaconis and Sly.

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Hoi H. Nguyen. "Random doubly stochastic matrices: The circular law." Ann. Probab. 42 (3) 1161 - 1196, May 2014. https://doi.org/10.1214/13-AOP877

Information

Published: May 2014
First available in Project Euclid: 26 March 2014

zbMATH: 1295.60009
MathSciNet: MR3189068
Digital Object Identifier: 10.1214/13-AOP877

Subjects:
Primary: 11P70, 15A52, 60G50

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 3 • May 2014
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