Open Access
2018 Circular law for the sum of random permutation matrices
Anirban Basak, Nicholas Cook, Ofer Zeitouni
Electron. J. Probab. 23: 1-51 (2018). DOI: 10.1214/18-EJP162


Let $P_n^1,\dots , P_n^d$ be $n\times n$ permutation matrices drawn independently and uniformly at random, and set $S_n^d:=\sum _{\ell =1}^d P_n^\ell $. We show that if $\log ^{12}n/(\log \log n)^{4} \le d=O(n)$, then the empirical spectral distribution of $S_n^d/\sqrt{d} $ converges weakly to the circular law in probability as $n \to \infty $.


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Anirban Basak. Nicholas Cook. Ofer Zeitouni. "Circular law for the sum of random permutation matrices." Electron. J. Probab. 23 1 - 51, 2018.


Received: 29 May 2017; Accepted: 27 March 2018; Published: 2018
First available in Project Euclid: 28 April 2018

zbMATH: 1386.15066
MathSciNet: MR3798243
Digital Object Identifier: 10.1214/18-EJP162

Primary: 15B52
Secondary: 15A18‎ , 60B10 , 60B20

Keywords: local laws , Logarithmic potential , random permutation , singular values , Stieltjes transform

Vol.23 • 2018
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