Elliptic Determinantal Processes and Elliptic Dyson Models
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Elliptic Determinantal Processes and Elliptic Dyson Models
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| Creator |
Katori, M.
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| 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.
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| Date |
2019-02-19T19:40:23Z
2019-02-19T19:40:23Z 2017 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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