The Porous Medium Equation: Multiscale Integrability in Large Deviations
- Authors: Benjamin Gess, Daniel Heydecker
- Preprint year: 2026
- First public date: 2026-02-10
- arXiv: 2602.09547
Abstract
We consider a zero-range process $η^N_t(x)$ with superlinear local jump rate, which in a hydrodynamic-small particle rescaling converges to the porous medium equation $\partial_t u=\frac12Δu^α, α>1$. As a main result we obtain a large deviation principle in any scaling regime of vanishing particle size $χ_N\to 0$. The key challenge is to develop uniform integrability estimate on the nonlinearity $(η^N(x))^α$ in a situation where neither pathwise regularity nor Dirichlet-form based regularity is readily available. We resolve this by introducing a novel multiscale argument exploiting the appearance of pathwise regularity across scales.
Associated SAiS members
Associated projects
Research areas
- Nonlinear PDEs
- Non-equilibrium Statistical Mechanics, Interacting Particle Systems and Fluctuating Hydrodynamics
BibTeX
@article{arxiv260209547,
title = {The Porous Medium Equation: Multiscale Integrability in Large Deviations},
author = {Benjamin Gess and Daniel Heydecker},
year = {2026},
eprint = {2602.09547},
archivePrefix = {arXiv},
primaryClass = {math.PR}
}