UBC Probability Seminar: Matthew Dickson

The random connection model (RCM) is a random graph model where the vertices are given by a Poisson point process with a given intensity, λ>0, and the edges exist independently with a probability that depends upon the relative positions of the two vertices in question. A standard example would be the Gilbert disc model. As we vary λ, we observe a percolation phase transition at a critical intensity λc>0. Finding λc is only possible in very exceptional cases, so here we investigate a high-dimension asymptotic expansion for the critical intensity that applies for a great variety of RCMs. This is based on arXiv:2309.08830 with Markus Heydenreich (Universität Augsburg).