JournalsrmiVol. 32, No. 2pp. 511–532

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

  • Rodolphe Garbit

    Université d'Angers, France
  • Kilian Raschel

    Université François Rabelais, Tours, France
On the exit time from a cone for random walks with drift cover
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Abstract

We compute the exponential decay of the probability that a given multi-dimensional random walk stays in a convex cone up to time nn, as nn 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.

Cite this article

Rodolphe Garbit, Kilian Raschel, On the exit time from a cone for random walks with drift. Rev. Mat. Iberoam. 32 (2016), no. 2, pp. 511–532

DOI 10.4171/RMI/893