Non-colliding Brownian bridges and the asymmetric tacnode process

Details Non-colliding Brownian bridges and the asymmetric tacnode process Non-colliding Brownian bridges and the asymmetric tacnode process

2011-12-21

arxiv.org/abs/1112.5002v2

Mathematics

Probability

21 pages, 1 figure, LaTeX; Includes a further representation of the kernel

Scientific paper

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).

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