Aldous' spectral gap phenomenon for the KMP model

Federico Sau (University of Milan) https://simons.berkeley.edu/talks/federico-sau-university-milan-2026-09-25 Local to Global Principles Aldous’ spectral gap conjecture, proved by Caputo, Liggett and Richthammer, states that, on any weighted graph, the spectral gaps of the interchange process and of the underlying random walk coincide. In this talk, we present an analogue for the Kipnis-Marchioro-Presutti (KMP) model on arbitrary weighted hypergraphs: its spectral gap is not identified with that of one random walk, but with that of a two-particle dual dynamics. This, in particular, settles a recent conjecture of Alon and Puder. Based on arXiv.2609.10450, joint work with Pietro Caputo and Matteo Quattropani (RomaTre).