Extremal Laws for Laplacian Random Matrices

2021/01/20 by Arenas-Velilla, Santiago, Pérez-Abreu, Victor
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2101.08318

Abstract

For an n× n Laplacian random matrix L with Gaussian entries it is proven that the fluctuations of the largest eigenvalue and the largest diagonal entry of L/√(n-1) are Gumbel. We first establish suitable non-asymptotic estimates and bounds for the largest eigenvalue of L in terms of the largest diagonal element of L. An expository review of existing results for the asymptotic spectrum of a Laplacian random matrix is also presented, with the goal of noting the differences from the corresponding classical results for Wigner random matrices. Extensions to Laplacian block random matrices are indicated.

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