Hydrodynamic limit of exclusion processes with killing on weighted Riemannian manifolds via a graph discretization
Abstract
In the present paper, we consider an exclusion process with killing on a proximity graph constructed from a partition of a geodesically complete weighted Riemannian manifold. We rigorously derive its hydrodynamic equation, which is governed by a heat equation with a killing potential term on the manifold. Within our graph discretization framework, we define an empirical density field for the exclusion process and prove its convergence, under an appropriate space-time scaling, to the unique bounded weak solution of the hydrodynamic equation, provided that the weighted manifold is stochastically complete. Combining local regularity for the parabolic equation with techniques from stochastic analysis on manifolds, we prove the uniqueness of the bounded weak solution and give the explicit representation of the solution in terms of the minimal Schrödinger kernel. Our result requires neither a global lower Ricci curvature bound nor global boundedness of the weight function.
Related
- A Weighted Discretization of Riemannian Manifolds with Lower Ricci Bounds
- Hydrodynamic limits of finite range exclusion processes
- Smoothness estimation for Whittle–Matérn processes on closed Riemannian manifolds
- Autoregressive Processes on Riemannian Manifolds
- Universal classical and quantum fluctuations in the large deviations of current of noisy quantum systems: Quantum symmetric simple exclusion and inclusion processes
BibTeX
@misc{ishiwata2026hydrodynamic,
title = {{Hydrodynamic limit of exclusion processes with killing on weighted Riemannian manifolds via a graph discretization}},
author = {Satoshi Ishiwata and Hiroshi Kawabi and Kenkichi Tsunoda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06892},
eprint = {2609.06892},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06892},
note = {CC0},
}
RIS
TY - UNPB
TI - Hydrodynamic limit of exclusion processes with killing on weighted Riemannian manifolds via a graph discretization
AU - Satoshi Ishiwata
AU - Hiroshi Kawabi
AU - Kenkichi Tsunoda
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.06892
UR - https://arxiv.org/abs/2609.06892
AB - In the present paper, we consider an exclusion process with killing on a proximity graph constructed from a partition of a geodesically complete weighted Riemannian manifold. We rigorously derive its hydrodynamic equation, which is governed by a heat equation with a killing potential term on the manifold. Within our graph discretization framework, we define an empirical density field for the exclusion process and prove its convergence, under an appropriate space-time scaling, to the unique bounded weak solution of the hydrodynamic equation, provided that the weighted manifold is stochastically complete. Combining local regularity for the parabolic equation with techniques from stochastic analysis on manifolds, we prove the uniqueness of the bounded weak solution and give the explicit representation of the solution in terms of the minimal Schrödinger kernel. Our result requires neither a global lower Ricci curvature bound nor global boundedness of the weight function.
ER -