t-Martin boundary of killed random walks in the quadrant

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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Cédric Lecouvey, Kilian Raschel. t-Martin boundary of killed random walks in the quadrant. Catherine Donati-Martin; Antoine Lejay; Alain Rouault. Séminaire de Probabilités XLVIII, Volume 2168 of the series Lecture Notes in Mathematics Springer, pp.305-323, 2016, Séminaire de Probabilités XLVIII, 978-3-319-44464-2. ⟨10.1007/978-3-319-44465-9_11⟩. ⟨hal-01199055v2⟩

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