Asymptotics of Weighted Reflectable Walks in $A_2$
Abstract
Lattice walks are used to model various physical phenomena. In particular, walks within Weyl chambers connect directly to representation theory via the Littelmann path model. We derive asymptotics for centrally weighted lattice walks within the Weyl chamber corresponding to by using tools from analytic combinatorics in several variables (ACSV). We find universality classes depending on the weights of the walks, in line with prior results on the weighted Gouyou-Beauchamps model. Along the way, we identify a type of singularity within a multivariate rational generating function that is not yet covered by the theory of ACSV. We conjecture asymptotics for this type of singularity.
Keywords
Cite
@article{arxiv.2405.13756,
title = {Asymptotics of Weighted Reflectable Walks in $A_2$},
author = {Torin Greenwood and Samuel Simon},
journal= {arXiv preprint arXiv:2405.13756},
year = {2024}
}
Comments
To appear in 2024 Analysis of Algorithms proceedings in the Leibniz International Proceedings in Informatics