Affiliation:
1. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University Tel Aviv Israel
Abstract
AbstractWe bound the second eigenvalue of random ‐regular graphs, for a wide range of degrees , using a novel approach based on Fourier analysis. Let be a uniform random ‐regular graph on vertices, and be its second largest eigenvalue by absolute value. For some constant and any degree with , we show that asymptotically almost surely. Combined with earlier results that cover the case of sparse random graphs, this fully determines the asymptotic value of for all . To achieve this, we introduce new methods that use mechanisms from discrete Fourier analysis, and combine them with existing tools and estimates on ‐regular random graphs—especially those of Liebenau and Wormald.
Subject
Applied Mathematics,Computer Graphics and Computer-Aided Design,General Mathematics,Software