Asymptotics of Weighted Reflectable Walks in A₂

2024/05/22 by Torin Greenwood, Greenwood, Torin, Samuel Simon +1
Mathematics · #05A16 (Primary) #05A16 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.2405.13756

openalex publication_date 2024/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

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