Elliptic determinantal process of type A

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• 作者：Makoto Katori
• 关键词：Noncolliding diffusion process ; Dyson’s Brownian motion model ; Elliptic determinant evaluations ; Determinantal process ; Determinantal martingale ; Alcove of affine Weyl group ; 60J65 ; 60G44 ; 82C22 ; 60B20 ; 33E05
• 刊名：Probability Theory and Related Fields
• 出版年：2015
• 出版时间：August 2015
• 年：2015
• 卷：162
• 期：3-4
• 页码：637-677
• 全文大小：738 KB
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• 作者单位：Makoto Katori (1)
  
  1. Department of Physics, Faculty of Science and Engineering, Chuo University, Bunkyo-ku, Tokyo, Kasuga, 112-8551, Japan
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Probability Theory and Stochastic Processes
  Mathematical and Computational Physics
  Quantitative Finance
  Mathematical Biology
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Operation Research and Decision Theory
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-2064

文摘

We introduce an elliptic extension of Dyson’s Brownian motion model, which is a temporally inhomogeneous diffusion process of noncolliding particles defined on a circle. Using elliptic determinant evaluations related to the reduced affine root system of type \(A\), we give determinantal martingale representation (DMR) for the process, when it is started at the configuration with equidistant spacing on the circle. DMR proves that the process is determinantal and the spatio-temporal correlation kernel is determined. By taking temporally homogeneous limits of the present elliptic determinantal process, trigonometric and hyperbolic versions of noncolliding diffusion processes are studied.