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Martin boundary of random walks in convex cones

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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https://hal.archives-ouvertes.fr/hal-02499786
Contributor : Kilian Raschel <>
Submitted on : Thursday, March 5, 2020 - 3:17:00 PM
Last modification on : Saturday, April 3, 2021 - 3:29:38 AM
Long-term archiving on: : Saturday, June 6, 2020 - 3:57:37 PM

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  • HAL Id : hal-02499786, version 1

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Jetlir Duraj, Kilian Raschel, Pierre Tarrago, Vitali Wachtel. Martin boundary of random walks in convex cones. 2020. ⟨hal-02499786⟩

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