Hydrodynamic limit of exclusion processes with killing on weighted Riemannian manifolds via a graph discretization
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institutions: Yamagata University, Keio University, Kyushu University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Analysis on metric measure spaces by optimal transport theory and Markov processes, Geometric analysis for non-symmetric generators on Riemannian manifolds, Equations with renormalization and stochastic analysis, Scaling limit for lattice-gas via precise estimates on relative entropies, Multifaceted Research on Stochastic Analysis on Infinite-Dimensional Spaces Integrating Perspectives from Geometric Analysis, 幾何解析の視点を融合した無限次元空間上の確率解析の新展開
OpenAlex ID: W7212057697