  The continuous-time random walk is defined as a Poissonization of
discrete-time random walk. We study the noncolliding system of continuous-time
simple and symmetric random walks on ${\mathbb{Z}}$. We show that the system is
determinantal for any finite initial configuration without multiple point. The
spatio-temporal correlation kernel is expressed by using the modified Bessel
functions. We extend the system to the noncolliding process with an infinite
number of particles, when the initial configuration has equidistant spacing of
particles, and show a relaxation phenomenon to the equilibrium determinantal
point process with the sine kernel.
