Energy exchange models, random walks and the KPZ class

par Guillaume Barraquand (LPENS)

jeudi 28 mai 2026, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (ICJ)

Kipnis, Marchioro, and Presutti (KMP) introduced in 1980 a very simple Markovian model for energy exchange in a chain of harmonic oscillators. In many ways, the KMP model behaves like the symmetric simple exclusion process (SSEP). The goal of this talk is to explain why, unlike the SSEP, the KMP model converges to the Kardar-Parisi-Zhang (KPZ) equation under a somewhat unusual scaling. The proof relies on the analysis of a random walk in a random environment associated with the KMP model. Thus, most of the talk will focus on explaining the connection between random walks in random environments and the KPZ class in spatial dimension 1. If time permits, I will report on some progress and conjectures in higher dimensions.