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math.PR2020
Reflected random walks and unstable Martin boundary
Irina Ignatiouk-Robert, Irina Kourkova, Kilian Raschel
We introduce a family of two-dimensional reflected random walks in the positive quadrant and study their Martin boundary. While the minimal boundary is systematically equal to a un…
math.PR2020
Martin boundary of random walks in convex cones
Jetlir Duraj, Kilian Raschel, Pierre Tarrago +1
We determine the asymptotic behavior of the Green function for zero-drift random walks confined to multidimensional convex cones. As a consequence, we prove that there is a unique…