Noncolliding diffusion processes reported in the present paper are
N-particle systems of diffusion processes in one-dimension, which are
conditioned so that all particles start from the origin and never collide with
each other in a finite time interval (0,T), 0<T<∞. We consider
four temporally inhomogeneous processes with duration T, the noncolliding
Brownian bridge, the noncolliding Brownian motion, the noncolliding
three-dimensional Bessel bridge, and the noncolliding Brownian meander. Their
particle distributions at each time t∈[0,T] are related to the
eigenvalue distributions of random matrices in Gaussian ensembles and in some
two-matrix models. Extreme values of paths in [0,T] are studied for these
noncolliding diffusion processes and determinantal and pfaffian representations
are given for the distribution functions. The entries of the determinants and
pfaffians are expressed using special functions.Comment: v2: LaTeX2e, 21 pages, 2 figures, correction mad