Recurrence and Scaling Limits in Vertex Reinforced Jump Processes on Dyson Hierarchical LatticesOberseminar Stochastics

by Prof. Xiaolin Zeng (Université de Strasbourg)

Thursday Jul 17, 2025, 4:30 PM → 5:30 PM Europe/Berlin

Endenicher Allee 60/0.011 - Seminarraum (Mathezentrum)

In this talk, we will introduce the vertex reinforced jump process on the Dyson
hierarchical lattice and define a closely related random Schrödinger operator.
We will demonstrate how to apply the fractional moment method, utilizing a
coarse-graining property of the sigma model, to show the recurrence of the
process. Additionally, we will discuss the fine-graining procedure, which pro-
vides an almost sure scaling limit of the spin model. Based on joint work with
Yichao Huang and Jinglin Wang.