### Abstract

Dyson's model is a one-dimensional system of Brownian motions with longrange 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 ℤ is occupied by one particle, to the stationary state, which is the determinantal point process with the sine kernel.

Original language | English |
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Pages (from-to) | 469-497 |

Number of pages | 29 |

Journal | Communications in Mathematical Physics |

Volume | 293 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2009 Sep 18 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics