  We study the dynamics of the outliers for a large number of independent
Brownian particles in one dimension. We derive the multi-time joint
distribution of the position of the rightmost particle, by two different
methods. We obtain the two time joint distribution of the maximum and second
maximum positions, and study the counting statistics at the edge. Finally we
derive the multi-time joint distribution of the running maximum, as well as the
joint distribution of the arrival time of the first particle at several space
points.
