A local central limit theorem for triangles in a random graph1. Issue 4 (12th February 2016) - Gilmer, Justin; Kopparty, Swastik
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