Circular law for the sum of random permutation matrices
© 2018, University of Washington. All rights reserved. Let Pn1, …, Pnd be n × n permutation matrices drawn independently and uniformly at random, and set Snd := ∑ℓ-1d Pnℓ. We show that if log12n/(log log n)4 ≤ d = O(n), then the empirical spectral distribution of Snd/√d converges weakly to the circular law in probability as n → ∞.
Basak, A; Cook, N; Zeitouni, O
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