$t$-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.

18 pages, 2 figures, to appear in Séminaire de Probabilités

References in corpus (4)

• Intervals in the greedy Tamari posets
• Counting quadrant walks via Tutte's invariant method
• Counting quadrant walks via Tutte's invariant method (extended abstract)
• Martin boundary of a killed random walk on ${\mathbb{Z}}_{+}^d$

Cited by in corpus (3)

• Weighted Lattice Walks and Universality Classes
• Constructing discrete harmonic functions in wedges
• Boundary behavior for random walks in cones