Local limit theorem for the number of K4 in G(n,p)

Seminar series

Combinatorial Theory Seminar

Date

Tue, 21 Nov 2017
16:00

Location

Speaker

Sophia Saller

Organisation

Oxford University

Understanding the distribution of subgraph counts has long been a central question in the study of random graphs. In this talk, we consider the distribution of Sn, the number of K4 subgraphs, in the Erdös Rényi random graph G(n, p). When the edge probability p \in (0, 1) is constant, a classical central limit theorem for Sn states that (Sn−µn)/σn converges in distribution. We establish a stronger form of convergence, namely the corresponding local limit theorem, which is joint work with O. Riordan.