arXiv Analytics

Sign in

arXiv:1201.4152 [math.PR]AbstractReferencesReviewsResources

Some exact asymptotics in the counting of walks in the quarter-plane

Guy Fayolle, Kilian Raschel

Published 2012-01-19, updated 2013-01-12Version 2

Enumeration of planar lattice walks is a classical topic in combinatorics, at the cross-roads of several domains (e.g., probability, statistical physics, computer science). The aim of this paper is to propose a new approach to obtain some exact asymptotics for walks confined to the quarter plane.

Comments: This article is the version 2 of http://fr.arxiv.org/abs/1201.4152v1 It provides an additional table giving a complete classification of the first singularities of the generating functions of interest; http://hal.inria.fr/hal-00765851
Journal: Discrete Mathematics and Theoretical Computer Science (2012) 109-124
Categories: math.PR
Subjects: 60G50, 30F10, 30D05
Related articles: Most relevant | Search more
arXiv:0902.2785 [math.PR] (Published 2009-02-16)
Random Walks in the Quarter Plane Absorbed at the Boundary : Exact and Asymptotic
arXiv:1408.3339 [math.PR] (Published 2014-08-14, updated 2014-11-10)
Random Walks in the Quarter-Plane: Advances in Explicit Criterions for the Finiteness of the Associated Group in the Genus 1 Case
arXiv:2003.02954 [math.PR] (Published 2020-03-05)
Exact asymptotics of component-wise extrema of two-dimensional Brownian motion

Links

Toolbox