In this talk, we prove a scaling limit for the size (both in terms of vertices and edges) of the largest components of a critical random intersection graph in which each individual is assigned to each community with a uniform probability p, all independently of each other. We show that the order of magnitude of the largest component depends significantly on the asymptotic behaviour of the ratio between the number of individuals and communities, while the limit random variables to which component sizes converge after rescaling are the same as in the Erdos-Renyi Random Graph. We further discuss how this result relates to the known scaling limits of critical inhomogeneous random graphs.

**Date**: 3 February 2020, 12:00 (Monday, 3rd week, Hilary 2020)**Venue**: Mathematical Institute

Woodstock Road OX2 6GGSee location on maps.ox**Details**: L4**Speaker**: Lorenzo Federico (University of Warwick)**Organising department**: Department of Statistics**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Public- Editor: Christina Goldschmidt