Skip to Main content Skip to Navigation
Journal articles

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

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.
Complete list of metadatas

Cited literature [24 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00838721
Contributor : Kilian Raschel <>
Submitted on : Saturday, March 21, 2015 - 1:41:11 PM
Last modification on : Monday, March 9, 2020 - 6:15:58 PM
Document(s) archivé(s) le : Monday, April 17, 2017 - 9:26:03 PM

File

ExponentialDecayForRandomWalk-...
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution 4.0 International License

Identifiers

Collections

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⟩

Share

Metrics

Record views

482

Files downloads

411