Random Doubly Stochastic Matrices: the Circular Law
نویسنده
چکیده
Let X be a matrix sampled uniformly from the set of doubly stochastic matrices of size n×n. We show that the empirical spectral distribution of the normalized matrix √ n(X − EX) converges almost surely to the circular law. This confirms a conjecture of Chatterjee, Diaconis and Sly.
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