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 (up to a multiplicative constant) there is a unique positive discrete harmonic function for these processes, in other words the Martin boundary is reduced to a singleton.
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https://hal.archives-ouvertes.fr/hal-01895793
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Submitted on : Monday, October 15, 2018 - 3:01:40 PM
Last modification on : Wednesday, January 15, 2020 - 1:40:33 AM
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  • HAL Id : hal-01895793, version 1
  • ARXIV : 1803.09253

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Kilian Raschel, Pierre Tarrago. Martin boundary of random walks in convex cones. 2018. ⟨hal-01895793⟩

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