Elliptic Determinantal Processes and Elliptic Dyson Models

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2017
• Main Author: Katori, M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149273
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Elliptic Determinantal Processes and Elliptic Dyson Models / M. Katori // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 43 назв. — англ.

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...