New harmonic-measure distribution functions of some simply connected planar regions in the complex plane

• Arunmaran Mahenthiram ^[1]
  1. [1] University of Jaffna

     University of Jaffna

     Sri Lanka

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 68, Nº. 2, 2025, págs. 459-483
• Idioma: inglés
• DOI: 10.33044/revuma.4038
• Enlaces
  • Texto completo
• Resumen

  • Consider a Brownian particle released from a fixed point z0 in a region Ω. The harmonic-measure distribution function, or h-function, h(r), expresses the probability that the Brownian particle first hits the boundary ∂Ω of the region Ω within distance r of z0. In this paper, we compute the h-function of several new planar simply connected two-dimensional regions by using two different methods, both involving conformal maps. We also explain the asymptotic behaviour at certain values of r where two different regimes meet.

    Moreover, for some regions, we examine how the behaviour of h(r) changes when part of the boundary changes.

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