Some exact asymptotics in the counting of walks in the quarter-plane
Guy Fayolle (INRIA Rocquencourt), Kilian Raschel (CNRS & LMPT,, Universit\'e Fran\c{c}ois Rabelais)
TL;DR
This paper introduces a novel approach to derive exact asymptotic formulas for counting lattice walks confined to the quarter plane, bridging combinatorics with probability and physics.
Contribution
It presents a new method for obtaining precise asymptotics of quarter-plane lattice walks, advancing the understanding of their enumeration.
Findings
Derived exact asymptotics for quarter-plane walks
Bridged combinatorics with probability and physics
Proposed a new analytical approach
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.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Advanced Combinatorial Mathematics · Markov Chains and Monte Carlo Methods