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

Abstract

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.

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