Orthogonal Dualities of Markov Processes and Unitary Symmetries
We study self-duality for interacting particle systems, where the particles move as continuous-time random walkers having either exclusion interaction or inclusion interaction. We show that orthogonal self-dualities arise from unitary symmetries of the Markov generator. For these symmetries, we prov...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2019 |
| Автори: | , , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210242 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Orthogonal Dualities of Markov Processes and Unitary Symmetries / G. Carinci, C. Franceschini, C. Giardinà, W. Groenevelt, F. Redig // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 32 назв. — англ. |
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Carinci, G. Franceschini, C. Giardinà, C. Groenevelt, W. Redig, F. 2025-12-04T13:09:43Z 2019 Orthogonal Dualities of Markov Processes and Unitary Symmetries / G. Carinci, C. Franceschini, C. Giardinà, W. Groenevelt, F. Redig // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 32 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 60J25; 82C22; 22E60 arXiv: 1812.08553 https://nasplib.isofts.kiev.ua/handle/123456789/210242 https://doi.org/10.3842/SIGMA.2019.053 We study self-duality for interacting particle systems, where the particles move as continuous-time random walkers having either exclusion interaction or inclusion interaction. We show that orthogonal self-dualities arise from unitary symmetries of the Markov generator. For these symmetries, we provide two equivalent expressions that are related by the Baker-Campbell-Hausdorff formula. The first expression is the exponential of an anti-Hermitian operator and thus is unitary by inspection; the second expression is factorized into three terms and is proved to be unitary by using generating functions. The factorized form is also obtained by using an independent approach based on scalar products, which is a new method of independent interest that we introduce to derive (bi)orthogonal duality functions from non-orthogonal duality functions. We thank the anonymous referees for their input, which helped to improve the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Orthogonal Dualities of Markov Processes and Unitary Symmetries Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Orthogonal Dualities of Markov Processes and Unitary Symmetries |
| spellingShingle |
Orthogonal Dualities of Markov Processes and Unitary Symmetries Carinci, G. Franceschini, C. Giardinà, C. Groenevelt, W. Redig, F. |
| title_short |
Orthogonal Dualities of Markov Processes and Unitary Symmetries |
| title_full |
Orthogonal Dualities of Markov Processes and Unitary Symmetries |
| title_fullStr |
Orthogonal Dualities of Markov Processes and Unitary Symmetries |
| title_full_unstemmed |
Orthogonal Dualities of Markov Processes and Unitary Symmetries |
| title_sort |
orthogonal dualities of markov processes and unitary symmetries |
| author |
Carinci, G. Franceschini, C. Giardinà, C. Groenevelt, W. Redig, F. |
| author_facet |
Carinci, G. Franceschini, C. Giardinà, C. Groenevelt, W. Redig, F. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We study self-duality for interacting particle systems, where the particles move as continuous-time random walkers having either exclusion interaction or inclusion interaction. We show that orthogonal self-dualities arise from unitary symmetries of the Markov generator. For these symmetries, we provide two equivalent expressions that are related by the Baker-Campbell-Hausdorff formula. The first expression is the exponential of an anti-Hermitian operator and thus is unitary by inspection; the second expression is factorized into three terms and is proved to be unitary by using generating functions. The factorized form is also obtained by using an independent approach based on scalar products, which is a new method of independent interest that we introduce to derive (bi)orthogonal duality functions from non-orthogonal duality functions.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210242 |
| citation_txt |
Orthogonal Dualities of Markov Processes and Unitary Symmetries / G. Carinci, C. Franceschini, C. Giardinà, W. Groenevelt, F. Redig // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 32 назв. — англ. |
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2025-12-07T21:24:52Z |
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