A collection of results relating the geometry of plane domains and the exit time of planar Brownian motion, II

Greg Markowsky; Clayton McDonald

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arXiv · 2506.09364

A collection of results relating the geometry of plane domains and the exit time of planar Brownian motion, II

Greg Markowsky·Clayton McDonald

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Abstract

This paper is the sequel to another with the same name (Buttigieg et al., Comput. Methods Funct. Theory, 2023), and is concerned with results of the same type. We deduce a result on the moments of the exit time of Brownian motion from domains whose boundary curve is replaced by a dashed line, and from domains arising from a periodic tiling of the plane. We also give a construction of a type of domain which is similar to a wedge domain, but the behaviour of whose exit time moments answer several questions that had been speculated upon.

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Greg Markowsky, Clayton McDonald. 2025-06-11. A collection of results relating the geometry of plane domains and the exit time of planar Brownian motion, II. https://arxiv.org/abs/2506.09364

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