Asymptotics for the number of zero drift reflectable walks in a Weyl chamber of type A

TL;DR

This paper derives asymptotic formulas for the number of zero drift lattice walks in a Weyl chamber of type A, connecting combinatorial models like vicious walkers with reflection methods.

Contribution

It provides new asymptotic results for zero drift lattice walks in Weyl chambers, extending and unifying previous formulas in the literature.

Findings

Asymptotic formulas for zero drift walks in Weyl chambers

Connection to lock step and random turns vicious walkers models

Extension of existing results in combinatorics and probability

Abstract

We study lattice walks in a Weyl chamber of type A with fixed or free end points. For lattice walk models with zero drift that may be counted by means of a reflection argument, we determine asymptotics for the number of such walks as their length tends to infinity. These models are equivalent to the lock step model and the random turns model of vicious walkers. As special cases, our main results include various asymptotic formulas found in the literature.