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

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.