Discrete harmonic functions in the three-quarter plane - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2020

Discrete harmonic functions in the three-quarter plane

Abstract

In this article we are interested in finding positive discrete harmonic functions with Dirichlet conditions in three quadrants. Whereas planar lattice (random) walks in the quadrant have been well studied, the case of walks avoiding a quadrant has been developed lately. We extend the method in the quarter plane – resolution of a functional equation via boundary value problem using a conformal mapping – to the three-quarter plane applying the strategy of splitting the domain into two symmetric convex cones. We obtain a simple explicit expression for the algebraic generating function of harmonic functions associated to random walks avoiding a quadrant.
Fichier principal
Vignette du fichier
harmonic_function-1.pdf (423.08 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02159567 , version 1 (18-06-2019)
hal-02159567 , version 2 (05-11-2020)

Identifiers

Cite

Amélie Trotignon. Discrete harmonic functions in the three-quarter plane. 2020. ⟨hal-02159567v2⟩
111 View
185 Download

Altmetric

Share

Gmail Facebook X LinkedIn More