Gespeichert in:
| Hauptverfasser: | , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2209.11114 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916153200214016 |
|---|---|
| author | Blyschak, Danyil Burke, Olivia Kuan, Jeffrey Li, Dennis Ustilovsky, Sasha Zhou, Zhengye |
| author_facet | Blyschak, Danyil Burke, Olivia Kuan, Jeffrey Li, Dennis Ustilovsky, Sasha Zhou, Zhengye |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_11114 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Orthogonal polynomial duality of a two-species asymmetric exclusion process Blyschak, Danyil Burke, Olivia Kuan, Jeffrey Li, Dennis Ustilovsky, Sasha Zhou, Zhengye Probability Mathematical Physics 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. |
| title | Orthogonal polynomial duality of a two-species asymmetric exclusion process |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2209.11114 |