Non-Equilibrium Dynamics of Dyson’s Model with an Infinite Number of Particles

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Abstract

Dyson’s model is a one-dimensional system of Brownian motions with long-range repulsive forces acting between any pair of particles with strength proportional to the inverse of distances with proportionality constant β/2. We give sufficient conditions for initial configurations so that Dyson’s model with β = 2 and an infinite number of particles is well defined in the sense that any multitime correlation function is given by a determinant with a continuous kernel. The class of infinite-dimensional configurations satisfying our conditions is large enough to study non-equilibrium dynamics. For example, we obtain the relaxation process starting from a configuration, in which every point of \({\mathbb{Z}}\) is occupied by one particle, to the stationary state, which is the determinantal point process with the sine kernel.

Keywords

Heat Kernel Dimensional Distribution Weyl Chamber Fredholm Determinant Correlation Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Physics, Faculty of Science and EngineeringChuo UniversityTokyoJapan
  2. 2.Department of Mathematics and Informatics, Faculty of ScienceChiba UniversityChibaJapan

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