Probability and Stochastic Analysis - University of Bonn

Abstract of "Non-colliding Brownian bridges and the asymmetric tacnode process"

with Bálint Vető.

We consider non-colliding Brownian bridges starting from two points and re- turning 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 λ > 0 of the limit shapes of the two families of bridges, (2) a parameter σ∈ℜ controlling the interaction on the fluctuation scale. This generalizes the result for the symmetric tacnode process (λ = 1 case).

Postscript file: [PS]

PDF file: [PDF]

arXiv: 1112.5002