Percolation on homogeneous graphs of polynomial growth

05.12.2022 16:15

Bernoulli percolation consists in erasing independently each edge of a graph G with some probability 1-p and studying the connected components (called clusters) of this random graph. Of interest is the parameter pc(G) above which infinite clusters exist. In this talk, we focus on homogeneous (= transitive) graphs for which the cardinality of balls is upper-bounded by a polynomial function of the radius. For such graphs, we get a good understanding of the supercritical regime p>pc (supercritical sharpness). From this, we deduce that Schramm's locality conjecture holds for such graphs: if you give me a ball of radius 10^10 of such a graph G, it is in principle possible for me to tell you "either pc(G)=1 or pc(G) is very close to [some specific value depending on the ball].

This is joint work with Daniel Contreras and Vincent Tassion.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Mathématique-Physique"

entrée libre