2024/12/12 by Ashwin Sah, Mehtaab Sawhney, Sah, Ashwin +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Statistical Methods and Inference #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2412.09535
Extending a previous result of the first two authors, we prove a local limit theorem for the joint distribution of subgraph counts in the Erdős-Rényi random graph G(n,p). This limit can be described as a nonlinear transformation of a multivariate normal distribution, where the components of the multivariate normal correspond to the graph factors of Janson. As an application, we show a number of results concerning the existence and enumeration of proportional graphs and related concepts, answering various questions of Janson and collaborators in the affirmative.