Affiliation:
1. Department of Mathematics Columbia University New York New York USA
2. Department of Mathematics Massachusetts Institute of Technology Cambridge Massachusetts USA
Abstract
Given a graph sequence and a simple connected subgraph , we denote by the number of monochromatic copies of in a uniformly random vertex coloring of with colors. We prove a central limit theorem for (we denote the appropriately centered and rescaled statistic as ) with explicit error rates. The error rates arise from graph counts of collections formed by joining copies of which we callgood joins. Good joins are closely related to the fourth moment of , which allows us to show afourth moment phenomenonfor the central limit theorem. For , we show that converges in distribution to whenever its fourth moment converges to 3. We show the convergence of the fourth moment is necessary to obtain a normal limit when .
Funder
National Science Foundation
Subject
Applied Mathematics,Computer Graphics and Computer-Aided Design,General Mathematics,Software