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

• Rodolphe Garbit ^[1] ; Kilian Raschel ^[1]
  1. [1] François Rabelais University

     François Rabelais University

     Arrondissement de Tours, Francia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 32, Nº 2, 2016, págs. 511-532
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.