English

$t$-Martin boundary of killed random walks in the quadrant

Probability 2016-12-30 v2

Abstract

We compute the tt-Martin boundary of two-dimensional small steps random walks killed at the boundary of the quarter plane. We further provide explicit expressions for the (generating functions of the) discrete tt-harmonic functions. Our approach is uniform in tt, and shows that there are three regimes for the Martin boundary.

Keywords

Cite

@article{arxiv.1509.04193,
  title  = {$t$-Martin boundary of killed random walks in the quadrant},
  author = {Cédric Lecouvey and Kilian Raschel},
  journal= {arXiv preprint arXiv:1509.04193},
  year   = {2016}
}

Comments

18 pages, 2 figures, to appear in S\'eminaire de Probabilit\'es