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
Datum:2024
Hauptverfasser: Floreani, Simone, Jansen, Sabine, Wagner, Stefan
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2024
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
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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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issn 1815-0659
language English
last_indexed 2026-03-16T12:07:09Z
publishDate 2024
publisher Інститут математики НАН України
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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.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Intertwinings for Continuum Particle Systems: an Algebraic Approach
Article
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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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