Limiting empirical spectral distribution for the non-backtracking matrix of an Erdős-Rényi random graph

Abstract

In this note, we give a precise description of the limiting empirical spectral distribution (ESD) for the non-backtracking matrices for an Erdős-Rényi graph assuming $np/\log n$ tends to infinity. We show that derandomizing part of the non-backtracking random matrix simplifies the spectrum considerably, and then we use Tao and Vu's replacement principle and the Bauer-Fike theorem to show that the partly derandomized spectrum is, in fact, very close to the original spectrum.

Final version. Accepted by Combinatorics, Probability and Computing

References in corpus (3)

• Stochastic blockmodels and community structure in networks
• Lectures on the local semicircle law for Wigner matrices
• Spectral radii of sparse random matrices

Cited by in corpus (2)

• Graph Distance from the Topological View of Non-backtracking Cycles
• Asymptotic absence of poles of Ihara zeta function of large Erdos-Renyi random graphs