Once reinforced random walk

15.04.2026, 13:00  –  Haus 9, Raum 0.17 und Zoom
Forschungsseminar Diskrete Spektraltheorie

Gady Kozma

Abstract: Once-reinforced random walk is a simple self-interacting process defined as follows. Edges that the walker already traversed at some point in the past are given a higher weight, 1+a for some a>0, compared to unvisited edges which are given weight 1. Sidoravicius' conjecture is that in dimension d>2 the process undergoes a phase transition in a. For small a it is diffusive and scales to Brownian motion, while for large a it is strictly subdiffusive and scales to Brownian motion reflected from the boundary of a slowly expanding balloon. We show the small a part of the conjecture, for d>5. Joint work with Dor Elboim.