Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP(2) and Multi-Species IRW
We obtain orthogonal polynomial self-duality functions for the multi-species version of the symmetric exclusion process (SEP(2)) and the independent random walker process (IRW) on a finite undirected graph. In each process, we have > 1 species of particles. In addition, we allow up to 2 particle...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
| ISSN: | 1815-0659 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211414 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP(2) and Multi-Species IRW. Zhengye Zhou. SIGMA 17 (2021), 113, 11 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We obtain orthogonal polynomial self-duality functions for the multi-species version of the symmetric exclusion process (SEP(2)) and the independent random walker process (IRW) on a finite undirected graph. In each process, we have > 1 species of particles. In addition, we allow up to 2 particles to occupy each site in the multi-species SEP(2). The duality functions for the multi-species SEP(2) and the multi-species IRW come from unitary intertwiners between different ∗-representations of the special linear Lie algebra ₙ₊₁ and the Heisenberg Lie algebra ₙ, respectively. The analysis leads to multivariate Krawtchouk polynomials as orthogonal duality functions for the multi-species SEP(2) and homogeneous products of Charlier polynomials as orthogonal duality functions for the multi-species IRW.
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| ISSN: | 1815-0659 |