Percolation Today is an online seminar aiming to promote the exchange of exciting new ideas on both Bernoulli and dependent percolation processes, at a level appropriate for specialists in the area. We hope to be a focal point to foster new connections and collaborations between the global community of percolation lovers.
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Critical cluster volumes in hierarchical percolation
Speaker: Tom Hutchcroft
Date: December 6th, 2022, 16.30 CET (no Webinar on Nov 29th)
Abstract: Hierarchical percolation is a toy model for percolation on Z^d that is expected to exhibit much of the same critical phenomena as percolation on Z^d, including having mean-field behaviour in high dimensions, non-mean-field behaviour with dimension-dependent exponents in low dimensions, and logarithmic corrections to mean-field behaviour at the upper-critical dimension. In this talk I will discuss my recent preprint https://arxiv.org/abs/2211.05686 in which a complete proof of this critical behaviour is established for the distribution of cluster volumes in all dimensions. In particular, I will discuss how one can implement what is in effect a rigorous Wilson-style renormalization group argument directly for percolation, without needing to reduce to some equivalent spin system. (Indeed, no such spin system is known to exist for percolation!) No previous experience with the renormalization group will be assumed.
Daniel Contreras Salinas
Pictures by: Adèle Ivain and Laurie Quétel