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).
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