Computing harmonic-measure distribution functions of some planar doubly connected regions
Volume 134 / 2025
Annales Polonici Mathematici 134 (2025), 187-206
MSC: Primary 30C20; Secondary 30C85
DOI: 10.4064/ap240724-12-4
Published online: 22 July 2025
Abstract
A harmonic-measure distribution function, or $h$-function, encodes the probability that a Brownian walker released from a fixed point in a region first hits the boundary of the region within a certain distance from the fixed point. We compute $h$-functions of several new planar doubly connected unbounded or bounded regions by using the $P$-function. Also, we cross-check our $h$-function graphs via numerical simulation.
