PreprintCC BY 4.0arXiv
Narrow escape problems beyond spherical holes: slits and tubes
Abstract
The narrow escape problem consists in characterizing the exit event of a Brownian motion trapped inside a domain with reflecting boundary and small absorbing holes. Using recent advances in the quasi-stationary distribution approach, we first give an explicit set of hypotheses that allows one to derive the asymptotics of the exit time and of the exit hole distribution. We then apply it in dimension three to several hole shapes: spherical holes, thin spheroidal holes shrinking to curves on the boundary (slits), and holes located at the end of thin tubes attached to the domain. We illustrate the accuracy of the results with numerical simulations, and extend them to higher dimensions.
Related
- A spectral approach to the narrow escape problem in two-dimensional domains
- The Two-Dimensional Narrow Escape Problem with Deterministic Initial Condition: Mean Escape Time and Escape location probabilities
- The narrow escape problem in arbitrary dimension
- Spherical Perfectly Matched Layer Method for Electromagnetic Scattering Problems with Large Wave Number
- Nonlinear stability of Schwarzschild black holes for the Einstein-massless Dirac system in spherical symmetry
BibTeX
@misc{carillo2026narrow,
title = {{Narrow escape problems beyond spherical holes: slits and tubes}},
author = {Louis Carillo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26514},
eprint = {2610.26514},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26514},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Narrow escape problems beyond spherical holes: slits and tubes
AU - Louis Carillo
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.26514
UR - https://arxiv.org/abs/2610.26514
AB - The narrow escape problem consists in characterizing the exit event of a Brownian motion trapped inside a domain with reflecting boundary and small absorbing holes. Using recent advances in the quasi-stationary distribution approach, we first give an explicit set of hypotheses that allows one to derive the asymptotics of the exit time and of the exit hole distribution. We then apply it in dimension three to several hole shapes: spherical holes, thin spheroidal holes shrinking to curves on the boundary (slits), and holes located at the end of thin tubes attached to the domain. We illustrate the accuracy of the results with numerical simulations, and extend them to higher dimensions.
ER -