Pathological Large Deviations of the KMP Process in Dimension $d\ge 2$
Probability
2026-05-27 v1 Analysis of PDEs
Abstract
We study dynamic large deviations for the Kipnis--Marchioro--Presutti process on the discrete torus . By recasting the candidate rate function in terms of a linear hyperbolic-parabolic equation with rough drift, we show that pathological trajectories appear in the large deviations with finite rate in any dimension . Along the way, we rigorously validate the lower bound derived by Bertini-Gabrielli-Lebowitz in any dimension.
Cite
@article{arxiv.2605.26652,
title = {Pathological Large Deviations of the KMP Process in Dimension $d\ge 2$},
author = {Daniel Heydecker},
journal= {arXiv preprint arXiv:2605.26652},
year = {2026}
}