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

Cédric Lecouvey; Kilian Raschel

doi:10.1007/978-3-319-44465-9_11

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arXiv · 1509.04193

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

Cédric Lecouvey·Kilian Raschel

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Abstract

We compute the $t$-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 $t$-harmonic functions. Our approach is uniform in $t$, and shows that there are three regimes for the Martin boundary.

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BibTeX RIS

Cédric Lecouvey, Kilian Raschel. 2015-09-14. $t$-Martin boundary of killed random walks in the quadrant. https://doi.org/10.1007/978-3-319-44465-9_11

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