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Limiting Directions for Random Walks in Classical Affine Weyl Groups

Aas, E and Ayyer, A and Linusson, S and Potka, S (2023) Limiting Directions for Random Walks in Classical Affine Weyl Groups. In: International Mathematics Research Notices, 2023 (4). pp. 3092-3137.

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Official URL: https://doi.org/10.1093/imrn/rnab317


Let W be a finite Weyl group and W̃ the corresponding affine Weyl group. A random element of W̃ can be obtained as a reduced random walk on the alcoves of W̃. By a theorem of Lam (Ann. Prob. 2015), such a walk almost surely approaches one of |W| many directions. We compute these directions when W is Bn, Cn, and Dn and the random walk is weighted by Kac and dual Kac labels. This settles Lam’s questions for types B and C in the affirmative and for type D in the negative. The main tool is a combinatorial two row model for a totally asymmetric simple exclusion process (TASEP) called the D∗-TASEP, with four parameters. By specializing the parameters in different ways, we obtain TASEPs for each of the Weyl groups mentioned above. Computing certain correlations in these TASEPs gives the desired limiting directions.

Item Type: Journal Article
Publication: International Mathematics Research Notices
Publisher: Oxford University Press
Additional Information: The copyright for this article belongs to the Authors.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 29 May 2023 03:10
Last Modified: 29 May 2023 03:10
URI: https://eprints.iisc.ac.in/id/eprint/81506

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