Martin boundary of random walks in convex cones

Jetlir Duraj; Kilian Raschel; Pierre Tarrago; Vitali Wachtel

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arXiv · 2003.03647

Martin boundary of random walks in convex cones

Jetlir Duraj·Kilian Raschel·Pierre Tarrago·Vitali Wachtel

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Abstract

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 positive discrete harmonic function for these processes (up to a multiplicative constant); in other words, the Martin boundary reduces to a singleton.

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Jetlir Duraj, Kilian Raschel, Pierre Tarrago, Vitali Wachtel. 2020-03-07. Martin boundary of random walks in convex cones. https://arxiv.org/abs/2003.03647

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