"Non-equilibrium dynamics of Dyson's model
with an infinite number of particles",
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.
