Nicholas A. Cook

activity

20182021

most citedNon-Hermitian random matrices with a variance profile (II): properties and examples

5 citations · 5 across the 2 of their papers we have counts for

collaborators

5 papers

math.PR2021

Universality of the minimum modulus for random trigonometric polynomials

Nicholas A. Cook, Hoi H. Nguyen

It has been shown in a recent work by Yakir-Zeitouni that the minimum modulus of random trigonometric polynomials with Gaussian coefficients has a limiting exponential distribution…

math.PR2020

Spectrum and pseudospectrum for quadratic polynomials in Ginibre matrices

Nicholas A. Cook, Alice Guionnet, Jonathan Husson

For a fixed quadratic polynomial $p$ in $n$ non-commuting variables, and $n$ independent $N \times N$ complex Ginibre matrices $X_{1}^{N}, \dots, X_{n}^{N}$ , we establish the conv…

math.PR2020★ 5 cited

Non-Hermitian random matrices with a variance profile (II): properties and examples

Nicholas A. Cook, Walid Hachem, Jamal Najim +1

For each $n$ , let $A_{n} = (σ_{ij})$ be an $n \times n$ deterministic matrix and let $X_{n} = (X_{ij})$ be an $n \times n$ random matrix with i.i.d. centered entries of unit variance. In the…

math.PR2018

Large deviations of subgraph counts for sparse Erdős--Rényi graphs

Nicholas A. Cook, Amir Dembo

For any fixed simple graph $H = (V, E)$ and any fixed $u > 0$ , we establish the leading order of the exponential rate function for the probability that the number of copies of $H$ in th…

math.PR2018

Maximum of the characteristic polynomial for a random permutation matrix

Nicholas Cook, Ofer Zeitouni

Let $P_{N}$ be a uniform random $N \times N$ permutation matrix and let $χ_{N} (z) = det (z I_{N} - P_{N})$ denote its characteristic polynomial. We prove a law of large numbers for the maximum…