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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2021 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2021
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211414 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862722240582254592 |
|---|---|
| author | Zhou, Zhengye |
| author_facet | Zhou, Zhengye |
| citation_txt | Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP(2) and Multi-Species IRW. Zhengye Zhou. SIGMA 17 (2021), 113, 11 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2026-03-21T04:33:38Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211414 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T04:33:38Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Zhou, Zhengye 2026-01-02T08:27:24Z 2021 Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP(2) and Multi-Species IRW. Zhengye Zhou. SIGMA 17 (2021), 113, 11 pages 1815-0659 2020 Mathematics Subject Classification: 60K35 arXiv:2110.07042 https://nasplib.isofts.kiev.ua/handle/123456789/211414 https://doi.org/10.3842/SIGMA.2021.113 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. The author is very grateful to Jeffrey Kuan and anonymous referees for helpful discussions and insightful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP(2) and Multi-Species IRW Article published earlier |
| spellingShingle | Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP(2) and Multi-Species IRW Zhou, Zhengye |
| title | Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP(2) and Multi-Species IRW |
| title_full | Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP(2) and Multi-Species IRW |
| title_fullStr | Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP(2) and Multi-Species IRW |
| title_full_unstemmed | Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP(2) and Multi-Species IRW |
| title_short | Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP(2) and Multi-Species IRW |
| title_sort | orthogonal polynomial stochastic duality functions for multi-species sep(2) and multi-species irw |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211414 |
| work_keys_str_mv | AT zhouzhengye orthogonalpolynomialstochasticdualityfunctionsformultispeciessep2andmultispeciesirw |