Intertwinings for Continuum Particle Systems: an Algebraic Approach
We develop the algebraic approach to duality, more precisely to intertwinings, within the context of particle systems in general spaces, focusing on the (1, 1) current algebra. We introduce raising, lowering, and neutral operators indexed by test functions, and we use them to construct unitary opera...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212261 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Intertwinings for Continuum Particle Systems: an Algebraic Approach. Simone Floreani, Sabine Jansen and Stefan Wagner. SIGMA 20 (2024), 046, 21 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862668553788850176 |
|---|---|
| author | Floreani, Simone Jansen, Sabine Wagner, Stefan |
| author_facet | Floreani, Simone Jansen, Sabine Wagner, Stefan |
| citation_txt | Intertwinings for Continuum Particle Systems: an Algebraic Approach. Simone Floreani, Sabine Jansen and Stefan Wagner. SIGMA 20 (2024), 046, 21 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We develop the algebraic approach to duality, more precisely to intertwinings, within the context of particle systems in general spaces, focusing on the (1, 1) current algebra. We introduce raising, lowering, and neutral operators indexed by test functions, and we use them to construct unitary operators, which act as self-intertwiners for some Markov processes having the Pascal process's law as a reversible measure. We show that such unitaries relate to generalized Meixner polynomials. Our primary results are continuum counterparts of results in the discrete setting obtained by Carinci, Franceschini, Giardinà, Groenevelt, and Redig (2019).
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| first_indexed | 2026-03-16T12:07:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212261 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T12:07:09Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Floreani, Simone Jansen, Sabine Wagner, Stefan 2026-02-03T07:56:54Z 2024 Intertwinings for Continuum Particle Systems: an Algebraic Approach. Simone Floreani, Sabine Jansen and Stefan Wagner. SIGMA 20 (2024), 046, 21 pages 1815-0659 2020 Mathematics Subject Classification: 60J25; 60K35; 82C22; 22E60 arXiv:2311.08763 https://nasplib.isofts.kiev.ua/handle/123456789/212261 https://doi.org/10.3842/SIGMA.2024.046 We develop the algebraic approach to duality, more precisely to intertwinings, within the context of particle systems in general spaces, focusing on the (1, 1) current algebra. We introduce raising, lowering, and neutral operators indexed by test functions, and we use them to construct unitary operators, which act as self-intertwiners for some Markov processes having the Pascal process's law as a reversible measure. We show that such unitaries relate to generalized Meixner polynomials. Our primary results are continuum counterparts of results in the discrete setting obtained by Carinci, Franceschini, Giardinà, Groenevelt, and Redig (2019). We thank the anonymous referees for their careful reading and helpful suggestions that helped improve the article. S.F. acknowledges financial support from the Engineering and Physical Sciences Research Council of the United Kingdom through the EPSRC Early Career Fellowship EP/V027824/1 and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy– EXC-2047/1– 390685813. S.J. and S.W. were supported under Germany’s excellence strategy EXC-2111-390814868. S.F. and S.W. thank the Hausdorff Institute for Mathematics (Bonn) for its hospitality during the Junior Trimester Program Stochastic modelling in life sciences funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy- EXC-2047/1390685813. The authors thank F. Redig for his insights at the beginning of the project. S.J. and S.W. thank T. Kuna and E. Lytvynov for helpful discussions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Intertwinings for Continuum Particle Systems: an Algebraic Approach Article published earlier |
| spellingShingle | Intertwinings for Continuum Particle Systems: an Algebraic Approach Floreani, Simone Jansen, Sabine Wagner, Stefan |
| title | Intertwinings for Continuum Particle Systems: an Algebraic Approach |
| title_full | Intertwinings for Continuum Particle Systems: an Algebraic Approach |
| title_fullStr | Intertwinings for Continuum Particle Systems: an Algebraic Approach |
| title_full_unstemmed | Intertwinings for Continuum Particle Systems: an Algebraic Approach |
| title_short | Intertwinings for Continuum Particle Systems: an Algebraic Approach |
| title_sort | intertwinings for continuum particle systems: an algebraic approach |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212261 |
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