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- W2949889969 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." @default.
- W2949889969 created "2019-06-27" @default.
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- W2949889969 date "2020-11-05" @default.
- W2949889969 modified "2023-09-27" @default.
- W2949889969 title "Discrete harmonic functions in the three-quarter plane" @default.
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