2020
DOI: 10.1016/j.aam.2020.102043
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The asymptotics of reflectable weighted walks in arbitrary dimension

Abstract: Gessel and Zeilberger generalized the reflection principle to handle walks confined to Weyl chambers, under some restrictions on the allowable steps. For some models that are invariant under the Weyl group action, they express the counting function for the walks with fixed starting and endpoint as a constant term in the Taylor series expansion of a rational function. Here, we focus on the simplest case, the Weyl groups A d 1 , which correspond to walks in the first orthant N d taking steps from a subset of {±1… Show more

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