A+ CATEGORY SCIENTIFIC UNIT

Computing harmonic-measure distribution functions of some planar doubly connected regions

Arunmaran Mahenthiram, Piriyalucksan Paramesvarampillai Annales Polonici Mathematici 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.

Authors

  • Arunmaran MahenthiramDepartment of Mathematics and Statistics
    University of Jaffna
    Jaffna 40000, Sri Lanka
    e-mail
  • Piriyalucksan ParamesvarampillaiDepartment of Mathematics and Statistics
    University of Jaffna
    Jaffna 40000, Sri Lanka
    e-mail

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