Discrepancy properties for random regular digraphs
Combinatorics
2015-10-27 v3 Probability
Abstract
For the uniform random regular directed graph we prove concentration inequalities for (1) codegrees and (2) the number of edges passing from one set of vertices to another. As a consequence, we can deduce discrepancy properties for the distribution of edges essentially matching results for Erd\H{o}s-R\'enyi digraphs obtained from Chernoff-type bounds. The proofs make use of the method of exchangeable pairs, developed for concentration of measure by Chatterjee. Exchangeable pairs are constructed using two involutions on the set of regular digraphs: a well-known "simple switching" operation, as well as a novel "reflection" operation.
Cite
@article{arxiv.1410.5595,
title = {Discrepancy properties for random regular digraphs},
author = {Nicholas A. Cook},
journal= {arXiv preprint arXiv:1410.5595},
year = {2015}
}
Comments
Minor changes based on referees' comments. To appear in Random Struct. Algor