Comparative Analyses of the Type D ASEP: Stochastic Fusion and Crystal Bases
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912224882196480 |
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| author | Brodsky, Erik Engel, Eva R. Panish, Connor Stolberg, Lillian |
| author_facet | Brodsky, Erik Engel, Eva R. Panish, Connor Stolberg, Lillian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21015 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Comparative Analyses of the Type D ASEP: Stochastic Fusion and Crystal Bases Brodsky, Erik Engel, Eva R. Panish, Connor Stolberg, Lillian Mathematical Physics Probability Quantum Algebra 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. |
| title | Comparative Analyses of the Type D ASEP: Stochastic Fusion and Crystal Bases |
| topic | Mathematical Physics Probability Quantum Algebra |
| url | https://arxiv.org/abs/2407.21015 |