Comparative Analyses of the Type D ASEP: Stochastic Fusion and Crystal Bases
Abstract
The Type D asymmetric simple exclusion process (ASEP) is a particle system involving two classes of particles that can be viewed from both a probabilistic and an algebraic perspective (arXiv:2011.13473). From a probabilistic perspective, we perform stochastic fusion on the Type D ASEP and analyze the outcome on generator matrices, limits of drift speed, stationary distributions, and Markov self-duality. From an algebraic perspective, we construct a fused Type D ASEP system from a Casimir element of , using crystal bases to analyze and manipulate various representations of . We conclude that both approaches produce different processes and therefore the previous method of arXiv:1908.02359, which analyzed the usual ASEP, does not generalize to all finite-dimensional simple Lie algebras.
Cite
@article{arxiv.2407.21015,
title = {Comparative Analyses of the Type D ASEP: Stochastic Fusion and Crystal Bases},
author = {Erik Brodsky and Eva R. Engel and Connor Panish and Lillian Stolberg},
journal= {arXiv preprint arXiv:2407.21015},
year = {2025}
}
Comments
81 pages, 7 figures. This research was conducted during a mathematics REU at Texas A&M University: an accessible version will be available at https://www.math.tamu.edu/reu/. Version 2: expanded the results of Lemma 3.3.1, and clarified the construction of the stochastic fusion matrix over a general number of fused sites. In addition, we condensed most of the proofs within the probability section