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

* Corresponding author
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.
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Journal articles
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Cited literature [24 references]

https://hal.archives-ouvertes.fr/hal-00838721
Contributor : Kilian Raschel Connect in order to contact the contributor
Submitted on : Saturday, March 21, 2015 - 1:41:11 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:09 PM
Long-term archiving on: : Monday, April 17, 2017 - 9:26:03 PM

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### Citation

Rodolphe Garbit, Kilian Raschel. On the exit time from a cone for random walks with drift. Revista Matemática Iberoamericana, European Mathematical Society, 2016, 32 (2), pp.511-532. ⟨10.4171/rmi/893⟩. ⟨hal-00838721v5⟩

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