On High Moments and the Spectral Norm of Large Dilute Wigner Random Matrices

TL;DR

This paper investigates the spectral norm behavior of large dilute Wigner matrices with a specific sparsity pattern, revealing asymptotic properties as the matrix size grows and the density parameter varies.

Contribution

It provides new asymptotic analysis of the spectral norm for dilute Wigner matrices with sparsity scaling as n^{-2/3(1+ε)}, extending understanding of spectral properties in sparse regimes.

Findings

Spectral norm scales on the order of n^{-2/3}

Asymptotic properties depend on the sparsity parameter ho_n

Results apply when ho_n is of order n^{-2/3(1+ε)} with ε > 0

Abstract

We consider a dilute version of the Wigner ensemble of n-dimensional random matrices H such that each row has in average \rho_n non-zero elements. We study asymptotic properties of the spectral norm of H on the scale n^{-2/3} in the limit when \rho_n is of the order n^{-2/3(1+\epsilon)} with \epsilon >0.