A graph discretized approximation of semigroups for diffusion with drift and killing on a complete Riemannian manifold
Functional Analysis
2023-08-17 v2 Differential Geometry
Probability
Abstract
In the present paper, we prove that the -semigroup generated by a Schr\"odinger operator with drift on a complete Riemannian manifold is approximated by the discrete semigroups associated with a family of discrete time random walks with killing in a flow on a sequence of proximity graphs, which are constructed by partitions of the manifold. Furthermore, when the manifold is compact, we also obtain a quantitative error estimate of the convergence. Finally, we give examples of the partition of the manifold and the drift term on two typical manifolds: Euclidean spaces and model manifolds.
Cite
@article{arxiv.2211.14472,
title = {A graph discretized approximation of semigroups for diffusion with drift and killing on a complete Riemannian manifold},
author = {Satoshi Ishiwata and Hiroshi Kawabi},
journal= {arXiv preprint arXiv:2211.14472},
year = {2023}
}