Corpus ID: 195069277

Discrete harmonic functions in the three-quarter plane

@article{Trotignon2019DiscreteHF,
  title={Discrete harmonic functions in the three-quarter plane},
  author={Am'elie Trotignon},
  journal={arXiv: Probability},
  year={2019}
}
  • Am'elie Trotignon
  • Published 2019
  • Mathematics
  • arXiv: Probability
  • 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… CONTINUE READING

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