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DOI: 10.4230/LIPIcs.AofA.2024.12
Asymptotics of Weighted Reflectable Walks in A₂

Authors: Torin Greenwood and Samuel Simon

Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)

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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Torin Greenwood and Samuel Simon. Asymptotics of Weighted Reflectable Walks in A₂. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{greenwood_et_al:LIPIcs.AofA.2024.12,
  author =	{Greenwood, Torin and Simon, Samuel},
  title =	{{Asymptotics of Weighted Reflectable Walks in A₂}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{12:1--12:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-329-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{302},
  editor =	{Mailler, C\'{e}cile and Wild, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.12},
  URN =		{urn:nbn:de:0030-drops-204472},
  doi =		{10.4230/LIPIcs.AofA.2024.12},
  annote =	{Keywords: Lattice walks, Weyl chambers, asymptotics weights, analytic combinatorics in several variables}
}
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