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Revista Matemática Iberoamericana

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Volume 32, Issue 2, 2016, pp. 511–532
DOI: 10.4171/RMI/893

Published online: 2016-06-08

On the exit time from a cone for random walks with drift

Rodolphe Garbit and Kilian Raschel[1]

(1) Université François Rabelais, Tours, France

We compute the exponential decay of the probability that a given multi-dimensional random walk stays in a convex cone up to time $n$, as $n$ goes to infinity. We show that the latter equals the minimum, on the dual cone, of the Laplace transform of the random walk increments. As an example, our results find applications in the counting of walks in orthants, a classical domain in enumerative combinatorics.

Keywords: Random walk, cones, exit time, Laplace transform

Garbit Rodolphe, Raschel Kilian: On the exit time from a cone for random walks with drift. Rev. Mat. Iberoam. 32 (2016), 511-532. doi: 10.4171/RMI/893