Publications [#350410] of Nicholas A Cook

Papers Published

1. Basak, A; Cook, N; Zeitouni, O, Circular law for the sum of random permutation matrices, Electronic Journal of Probability, vol. 23 (January, 2018) [doi]
   (last updated on 2026/01/15)

   Abstract:
   Let Pn¹, …, Pn^d be n × n permutation matrices drawn independently and uniformly at random, and set Sn^d := ∑ℓ-1^d Pn^ℓ. We show that if log¹²n/(log log n)⁴ ≤ d = O(n), then the empirical spectral distribution of Sn^d/√d converges weakly to the circular law in probability as n → ∞.