Asymptotics of Weighted Reflectable Walks in $A_2$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917673523216384 |
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| author | Greenwood, Torin Simon, Samuel |
| author_facet | Greenwood, Torin Simon, Samuel |
| contents | 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 $A_2$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13756 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotics of Weighted Reflectable Walks in $A_2$ Greenwood, Torin Simon, Samuel Combinatorics 05A16 (Primary), 05A16 (Secondary) 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 $A_2$ 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. |
| title | Asymptotics of Weighted Reflectable Walks in $A_2$ |
| topic | Combinatorics 05A16 (Primary), 05A16 (Secondary) |
| url | https://arxiv.org/abs/2405.13756 |