Boundary behavior of random walks in cones

Kilian Raschel (1, 2) , Pierre Tarrago (3)

1 IDP - Institut Denis Poisson
2 CNRS - Centre National de la Recherche Scientifique
3 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

We study the asymptotic behavior of zero-drift random walks confined to multidimensional convex cones, when the endpoint is close to the boundary. We derive a local limit theorem in the fluctuation regime.

Mots clés: Random walk; cone; exit time; harmonic function; Brownian motion; coupling; heat kernel

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

Kilian Raschel, Pierre Tarrago. Boundary behavior of random walks in cones. Markov Processes And Related Fields, 2020, 26 (4), pp.711--756. ⟨hal-01895793v2⟩