Spectral Gap for the Stochastic Exchange Model
Probability
2025-07-18 v2
Abstract
We prove a spectral gap inequality for the stochastic exchange model studied by Gaspard and Gilbert and by Grigo, Khanin and Sz\'asz in connection with understanding heat conduction in a deterministic billiards model. The bound on the spectral gap that we prove is uniform in the number of particles, as had been conjectured. We adapt techniques that were originally developed to prove spectral gap bounds for the Kac model with hard sphere collisions, which, like the stochastic exchange model, has degenerate jump rates.
Cite
@article{arxiv.2504.13533,
title = {Spectral Gap for the Stochastic Exchange Model},
author = {Eric A. Carlen and Gustavo Posta and Imre Péter Tóth},
journal= {arXiv preprint arXiv:2504.13533},
year = {2025}
}
Comments
This revision corrects some typos in the previous version