$t$-Martin boundary of killed random walks in the quadrant
Probability
2016-12-30 v2
Abstract
We compute the -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 -harmonic functions. Our approach is uniform in , 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