Dynamical interface above a hard wall and reflected SPDE on the half-line
Probability
2025-09-04 v1
Abstract
We consider a dynamical random interface on the infinite lattice evolving according to a "corner flip" dynamic above a hard wall, with an additional pinning at the origin. We study the stationary fluctuations under a diffusive scaling and prove convergence in law towards the solution of an SPDE of Nualart-Pardoux's type, namely the Reflected Stochastic Heat Equation on the half-line. We also obtain that the law of the 3-dimensional Bessel process is an invariant measure for this SPDE.
Cite
@article{arxiv.2509.03328,
title = {Dynamical interface above a hard wall and reflected SPDE on the half-line},
author = {Pierre Faugère and Cyril Labbé},
journal= {arXiv preprint arXiv:2509.03328},
year = {2025}
}