Martin boundary of random walks in convex cones
Annales Henri Lebesgue, Volume 5 (2022), pp. 559-609.

KeywordsRandom walk; cone; exit time; Green function; harmonic function; Martin boundary; Brownian motion; coupling

### 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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