Discrepancy properties for random regular digraphs. Issue 1 (1st March 2016)

• Record Type: Journal Article
• Authors: Cook, Nicholas A.
• Is Part Of: Random structures & algorithms. Volume 50:Issue 1(2017)
• Page Start: 23
• Page End: 58
• Publication Date: 2016-03-01
• Subjects: random regular graph -- discrepancy property -- concentration of measure -- method of exchangeable pairs; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20643
• Languages: English
• ISSNs: 1042-9832

Abstract

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 Erdős–Rényi digraphs obtained from Chernoff‐type bounds. The proofs make use of the method of exchangeable pairs, developed for concentration of measure by Chatterjee in (Chatterjee, Probab Theory and Relat Fields 138 (2007), 305–321). 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. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 23–58, 2017