English

Discrete harmonic functions in Lipschitz domains

Probability 2019-04-23 v2

Abstract

We prove the existence and uniqueness of a discrete nonnegative harmonic function for a random walk satisfying finite range, centering and ellipticity conditions, killed when leaving a globally Lipschitz domain in Zd\mathbb{Z}^d. Our method is based on a systematic use of comparison arguments and discrete potential-theoretical techniques.

Keywords

Cite

@article{arxiv.1901.00637,
  title  = {Discrete harmonic functions in Lipschitz domains},
  author = {Sami Mustapha and Mohamed Sifi},
  journal= {arXiv preprint arXiv:1901.00637},
  year   = {2019}
}

Comments

11 pages

R2 v1 2026-06-23T07:02:02.328Z