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Expanding the Critical Intensity of Random Connection Models

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SSD - Stochastic systems for anomalous diffusion

Random connection models (RCMs) are random graph models where the vertices are given by a Poisson point process with a given intensity, $\lambda>0$, and the edges exist independently with a probability that depends upon the relative positions of the two vertices in question. These models include ``Poisson blob models”, such as the Gilbert disc model. As we vary $\lambda$, we observe a percolation phase transition at a critical intensity $\lambda_c>0$. Finding this critical value is only possible in very exceptional cases, so here we use the lace expansion for RCMs (as found by Heydenreich, van der Hofstad, Last, and Matzke 2019) to find a high-dimension asymptotic expansion for the critical intensity. This is based on arXiv:2309.08830 with Markus Heydenreich (Universit{\”a}t Augsburg)

This talk is part of the Isaac Newton Institute Seminar Series series.

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