Martin boundary of random walks in convex cones

Kilian Raschel (1) , Pierre Tarrago (2)

1 IDP - Institut Denis Poisson
2 CIMAT - Centro de Investigación en Matemáticas

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.

Domaines: Probabilités [math.PR]; Combinatoire [math.CO]

Kilian Raschel, Pierre Tarrago. Martin boundary of random walks in convex cones. 2018. ⟨hal-01895793v1⟩