Analysis and Probability seminar

Abstract: The study of certain observables in statistical mechanics models on trees can often be reduced to the analysis of recursive relations, as is the case for the survival probability of the random cluster model. When this recursion is concave, it can be compared to that of effective conductances (possibly nonlinear) between the root and the leaves of the tree. In joint work with Quentin Berger (Sorbonne Paris-Nord), we determine the precise asymptotic behavior of such nonlinear conductances on Bienaymé–Galton–Watson trees. This yields detailed information on the critical behavior of the random cluster model on these trees.