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.
Citation
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
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