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Elliptic Determinantal Processes and Elliptic Dyson Models
We introduce seven families of stochastic systems of interacting particles in one-dimension corresponding to the seven families of irreducible reduced affine root systems. We prove that they are determinantal in the sense that all spatio-temporal correlation functions are given by determinants contr...
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Інститут математики НАН України
2017
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/149273 |
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irk-123456789-1492732019-02-20T01:23:57Z Elliptic Determinantal Processes and Elliptic Dyson Models Katori, M. We introduce seven families of stochastic systems of interacting particles in one-dimension corresponding to the seven families of irreducible reduced affine root systems. We prove that they are determinantal in the sense that all spatio-temporal correlation functions are given by determinants controlled by a single function called the spatio-temporal correlation kernel. For the four families AN₋₁, BN, CN and DN, we identify the systems of stochastic differential equations solved by these determinantal processes, which will be regarded as the elliptic extensions of the Dyson model. Here we use the notion of martingales in probability theory and the elliptic determinant evaluations of the Macdonald denominators of irreducible reduced affine root systems given by Rosengren and Schlosser. 2017 Article Elliptic Determinantal Processes and Elliptic Dyson Models / M. Katori // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 43 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 60J65; 60G44; 82C22; 60B20; 33E05; 17B22 DOI:10.3842/SIGMA.2017.079 http://dspace.nbuv.gov.ua/handle/123456789/149273 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
We introduce seven families of stochastic systems of interacting particles in one-dimension corresponding to the seven families of irreducible reduced affine root systems. We prove that they are determinantal in the sense that all spatio-temporal correlation functions are given by determinants controlled by a single function called the spatio-temporal correlation kernel. For the four families AN₋₁, BN, CN and DN, we identify the systems of stochastic differential equations solved by these determinantal processes, which will be regarded as the elliptic extensions of the Dyson model. Here we use the notion of martingales in probability theory and the elliptic determinant evaluations of the Macdonald denominators of irreducible reduced affine root systems given by Rosengren and Schlosser. |
| format |
Article |
| author |
Katori, M. |
| spellingShingle |
Katori, M. Elliptic Determinantal Processes and Elliptic Dyson Models Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Katori, M. |
| author_sort |
Katori, M. |
| title |
Elliptic Determinantal Processes and Elliptic Dyson Models |
| title_short |
Elliptic Determinantal Processes and Elliptic Dyson Models |
| title_full |
Elliptic Determinantal Processes and Elliptic Dyson Models |
| title_fullStr |
Elliptic Determinantal Processes and Elliptic Dyson Models |
| title_full_unstemmed |
Elliptic Determinantal Processes and Elliptic Dyson Models |
| title_sort |
elliptic determinantal processes and elliptic dyson models |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149273 |
| citation_txt |
Elliptic Determinantal Processes and Elliptic Dyson Models / M. Katori // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 43 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT katorim ellipticdeterminantalprocessesandellipticdysonmodels |
| first_indexed |
2023-05-20T17:31:27Z |
| last_indexed |
2023-05-20T17:31:27Z |
| _version_ |
1796153494779985920 |