Trees, forests and Doob transform ( Lucas Rey, Paris)

16.12.2024 16:15 – 18:00

Abstract:
The study of spanning trees dates back at least to the matrix-tree theorem of Kirchoff (1847). This theorem gives a determinantal formula for the number of spanning trees of a given graph. The study of random spanning trees (RST) was pushed further, using tools such as the transfer current theorem, or the Wilson’s algorithm which samples RST using random walks. Another important tool for planar graphs is the Temperley’s bijection between spanning trees and dimer covers of an associated graph. More recently, in dimension 2, the scaling limit was established by Werner, Schramm, Lawler (2004) and universality results were also proved.
Spanning forests generalize spanning trees, and some of the tools mentioned above (but not all !) also apply to forests.
In this talk, we will explain how to use the Doob transform (or h-transform) to transfer the tools from the trees to the forests. As an application, we will present a universality result for the near-critical scaling limit of the RST model in dimension 2.

Lieu

Conseil Général 7-9, Room 1-15, Séminaire Math Physics

entrée libre