Abstract : 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.
https://hal.archives-ouvertes.fr/hal-00838721
Contributeur : Kilian Raschel
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Soumis le : samedi 21 mars 2015 - 13:41:11
Dernière modification le : mercredi 21 mars 2018 - 10:54:03
Document(s) archivé(s) le : lundi 17 avril 2017 - 21:26:03
