A local central limit theorem for triangles in a random graph1. Issue 4 (12th February 2016)

• Record Type: Journal Article
• Authors: Gilmer, Justin; Kopparty, Swastik
• Is Part Of: Random structures & algorithms. Volume 48:Issue 4(2016)
• Page Start: 732
• Page End: 750
• Publication Date: 2016-02-12
• Subjects: Random Graphs -- local limit theorem -- subgraph counts -- characteristic function; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20604
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract: In this paper, we prove a local limit theorem for the distribution of the number of triangles in the Erdos‐Rényi random graph G ( n, p ), where p ∈ ( 0, 1 ) is a fixed constant. Our proof is based on bounding the characteristic function ψ ( t ) of the number of triangles, and uses several different conditioning arguments for handling different ranges of t . © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 48, 732–750, 2016