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

2024/07/30 by Brodsky, Erik, Engel, Eva R., Panish, Connor +1 · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2407.21015

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(so₆), using crystal bases to analyze and manipulate various representations of U_q(so₆). 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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