01:01:00
published on July 3, 2025
Coulomb gas approach to conformal field theory and lattice models of 2D statistical physics
By Stanislav Smirnov
The infinite bin model, old and new
Appears in collection : Perfectly matched perspectives on statistical mechanics, combinatorics and geometry / Perspectives couplées sur la mécanique statistique, la combinatoire et la géométrie
The infinite bin model (IBM) is a family of ranked-biased branching random walks on the integers, parameterized by a probability distribution on positive integers. Alternatively it may be seen as a family of interacting particle systems, depicted as balls inside bins. The speed of the front of the IBM depends on the probability distribution which parameterizes it. I will first review some special cases that have been known for some time: the IBM parameterized by the uniform distribution on some finite interval of integers [1,N], which is nothing but a branching random walk with selection, and the IBM parameterized by a geometric distribution, which can be coupled with last passage percolation on the complete graph. Then I will discuss long memory properties of the IBM, in particular whether a site may reproduce infinitely often or not. Finally I will discuss a hydrodynamic limit of the IBM where one can explicitly compute the speed of the front. In that case, a wall-crossing phenomenon appears and Dyck paths come into play. The talk is based on joint works with Bastien Mallein (Université Toulouse III Paul Sabatier), Arvind Singh (CNRS and Université Paris-Saclay) and Benjamin Terlat (Université Paris-Saclay).
