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PreprintCC BY 4.0arXiv

A spectral approach to the narrow escape problem in two-dimensional domains

  • Louis Carillo
  • Tony Lelièvre
  • Thomas Normand
  • Urbain Vaes
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Abstract

We study the law of the exit time and exit point of a Brownian motion in a two-dimensional domain with reflecting boundary conditions, except on small disjoint exit windows through which the stochastic process can escape the domain. In the limit of infinitely small exit windows, it is natural to assume that the process starts from the quasi-stationary distribution. In this setting, we obtain a precise description of the exit event.

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Cite

BibTeXRIS
BibTeX
@misc{carillo2026spectral,
  title = {{A spectral approach to the narrow escape problem in two-dimensional domains}},
  author = {Louis Carillo and Tony Lelièvre and Thomas Normand and Urbain Vaes},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.05007},
  eprint = {2608.05007},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.05007},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A spectral approach to the narrow escape problem in two-dimensional domains
AU  - Louis Carillo
AU  - Tony Lelièvre
AU  - Thomas Normand
AU  - Urbain Vaes
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2608.05007
UR  - https://arxiv.org/abs/2608.05007
AB  - We study the law of the exit time and exit point of a Brownian motion in a two-dimensional domain with reflecting boundary conditions, except on small disjoint exit windows through which the stochastic process can escape the domain. In the limit of infinitely small exit windows, it is natural to assume that the process starts from the quasi-stationary distribution. In this setting, we obtain a precise description of the exit event.
ER  -