Random forests and fermionic field theories
Kick-off event on Wed 29.10.25 at Institut Henri Poincaré. Inscriptions: link indico
The seminars at IHES will take place on the following Wednesdays: 12.11, 26.11 and 10.12, see program
Supercritical frozen Erdős-Rényi and uniform random forests
byVincent Viau
Abstract:The frozen Erdős-Rényi random graph is a variant of the standard dynamical Erdős-Rényi random graph that prevents the creation of the giant component by freezing the evolution of connected components with a unique cycle. The formation of multicyclic components is forbidden, and the growth of components with a unique cycle is slowed down, depending on a parameter \(p \in [0, 1]\) that quantifies the slowdown. In this talk, we will study the fluid limit of the main statistics of this process, that is their functional convergence as the number of vertices of the graph becomes large and after a proper rescaling, to the solution of a system of differential equations. The proof is based on the free forest property of the frozen model: the forest part of the graph is a uniform random forest. In order to prove the fluid limit results, we will explain how to study and count forests using conditioned random walks.
All talks Fall '25: random forests and fermionic field theories