Orthogonal polynomial duality of a two-species asymmetric exclusion process

Autor: Blyschak, Danyil, Burke, Olivia, Kuan, Jeffrey, Li, Dennis, Ustilovsky, Sasha, Zhou, Zhengye
Rok vydání: 2022
Předmět:
Zdroj: J Stat Phys 190, 101 (2023)
Druh dokumentu: Working Paper
DOI: 10.1007/s10955-023-03100-y
Popis: We examine type D ASEP, a two--species interacting particle system which generalizes the usual asymmetric simple exclusion process. For certain cases of type D ASEP, the process does not give priority for one species over another, even though there is nontrivial interaction between the two species. For those specific cases, we prove that the type D ASEP is self--dual with respect to an independent product of $q$--Krawtchouk polynomials. The type D ASEP was originally constructed in arXiv:2011.13473, using the type D quantum groups $\mathcal{U}_q(\mathfrak{so}_6)$ and $\mathcal{U}_q(\mathfrak{so}_8)$. That paper claimed that certain states needed to be "discarded'' in order to ensure non--negativity. Here, we also provide a more efficient argument for the same claim.
Comment: Version 2 is the journal version. To obtain an accessible version of the PDF, please visit http://math.tamu.edu/~jkuan/arXiv-2209.11114.html
Databáze: arXiv
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