  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
$\beta/2$. We give sufficient conditions for initial configurations so that
Dyson's model with $\beta=2$ 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.
