Probability and Stochastic Analysis Seminar  RSS

20/09/2023, 17:00 — 18:00 — Online
Matteo D'Achille, LMO Université Paris-Saclay

Almost Gibbsian Measures on a Cayley Tree

The ferromagnetic Ising model on infinite regular trees has a longstanding tradition in Probability and Statistical Mechanics. As such, it offers a solid benchmark in the quest for putting Renormalization Group ideas from Physics on rigorous grounds. In this talk, I will introduce a mapping on Ising configurations on the 3-regular infinite tree, namely a modified majority rule transformation, which was already known to lead to non-Gibbsian measures at any temperature. However, we show that the renormalized measure, whose properties can be studied thanks to a model of percolation of zeros, actually satisfies at any temperature an almost sure version of Gibbsianity, which we call almost-Gibbsianity. Key ingredients of the discussion will be the celebrated Kozlov-Sullivan Theorem for Gibbsian specifications, the recursivity inherent to the treatment on trees and temperature-dependent bond percolation. Talk mostly based on a joint paper with Arnaud Le Ny (Markov Process. Relat. Fields 28, 2022)

Except for a few of the oldest sessions these are from the Seminário de Probabilidade e Mecânica Estatística at IMPA which is co-sponsored by several institutions, in particular Instituto Superior Técnico.