2026-07-23T22:06:48Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:20447 2024-07-18T12:12:42Z ddc:004 open_access

Asymptotics of Weighted Reflectable Walks in A₂ Greenwood, Torin Simon, Samuel Lattice walks Weyl chambers asymptotics weights analytic combinatorics in several variables 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 A₂ 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Torin Greenwood and Samuel Simon 2024 Is Part Of LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.AofA.2024.12 urn:nbn:de:0030-drops-204472 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.12 eng https://creativecommons.org/licenses/by/4.0/legalcode