1112.5002 (Patrik L. Ferrari et al.)

Non-colliding Brownian bridges and the asymmetric tacnode process    [PDF]

Patrik L. Ferrari, Balint Veto

We consider non-colliding Brownian bridges starting from two points and
returning to the same position. These positions are chosen such that, in the
limit of large number of bridges, the two families of bridges just touch each
other forming a tacnode. We obtain the limiting process at the tacnode, the
"asymmetric tacnode process". It is a determinantal point process with
correlation kernel given by two parameters: (1) the curvature's ratio \lambda>0
of the limit shapes of the two families of bridges, (2) a parameter \sigma
controlling the interaction on the fluctuation scale. This generalizes the
result for the symmetric tacnode process (\lambda=1 case).

View original: http://arxiv.org/abs/1112.5002