  We consider n one-dimensional Brownian motions, such that n/2 Brownian
motions start at time t=0 in the starting point a and end at time t=1 in the
endpoint b and the other n/2 Brownian motions start at time t=0 at the point -a
and end at time t=1 in the point -b, conditioned that the n Brownian paths do
not intersect in the whole time interval (0,1). The correlation functions of
the positions of the non-intersecting Brownian motions have a determinantal
form with a kernel that is expressed in terms of multiple Hermite polynomials
of mixed type. We analyze this kernel in the large n limit for the case ab<1/2.
We find that the limiting mean density of the positions of the Brownian motions
is supported on one or two intervals and that the correlation kernel has the
usual scaling limits from random matrix theory, namely the sine kernel in the
bulk and the Airy kernel near the edges.
