English

The narrow capture problem on general Riemannian surfaces

Probability 2022-09-27 v1 Analysis of PDEs Differential Geometry

Abstract

In this article, we study the narrow capture problem on a Riemannian 2-manifold. This involves the derivation of the mean first passage (sojourn) time of a surface-bound ion modelled as a Brownian particle. We use a layer potential argument in conjunction with microlocal analysis in order to derive the leading order singularity as well as the O(1) term of the mean first passage time and the associated spatial average.

Keywords

Cite

@article{arxiv.2209.12425,
  title  = {The narrow capture problem on general Riemannian surfaces},
  author = {Medet Nursultanov and William Trad and Justin C. Tzou and Leo Tzou},
  journal= {arXiv preprint arXiv:2209.12425},
  year   = {2022}
}

Comments

22 pages

R2 v1 2026-06-28T02:04:25.983Z