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arXiv · 2407.21015

Comparative Analyses of the Type D ASEP: Stochastic Fusion and Crystal Bases

Erik Brodsky·Eva R. Engel·Connor Panish·Lillian Stolberg
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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 $U_q(so_6)$, using crystal bases to analyze and manipulate various representations of $U_q(so_6)$. 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.

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Erik Brodsky, Eva R. Engel, Connor Panish, Lillian Stolberg. 2024-07-30. Comparative Analyses of the Type D ASEP: Stochastic Fusion and Crystal Bases. https://arxiv.org/abs/2407.21015

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