25/03/2026, 16:00 — 17:00 Europe/Lisbon —
Online
Alexander Glazman, University of Innsbruck
Graphical representations of 2D models
The seminal Edwards-Sokal coupling allows to express correlations in the Potts model via connection probabilities in the random-cluster model. In this talk we discuss how similar ideas can be applied in a number of other settings. Specifically: - the planar Potts model can be related to the Ashkin-Teller model, and this brings new results for both models, including convergence of interfaces to Brownian bridges and the wetting phenomenon (j.w. Moritz Dober and Sébastien Ott); - the loop O(n) model can be resampled via a divide-and-color procedure, and this can be used to establish a big part of its phase diagram. Another important ingredient is our proof of a conjecture of Benjamini and Schramm - in particular, we show that p_c is at least 1/2 on any unimodular invariantly amenable planar graph (j.w. Matan Harel and Nathan Zelesko); - we also show delocalisation of two-dimensional height functions related to these models (j.w. Piet Lammers).
