Non-colliding Brownian Motions and the extended tacnode process

Details Non-colliding Brownian Motions and the extended tacnode process Non-colliding Brownian Motions and the extended tacnode process

2011-05-20

arxiv.org/abs/1105.4027v3

Mathematics

Probability

38 pages. In the revised version a few arguments have been expanded and many typos corrected

Scientific paper

We consider non-colliding Brownian motions with two starting points and two endpoints. The points are chosen so that the two groups of Brownian motions just touch each other, a situation that is referred to as a tacnode. The extended kernel for the determinantal point process at the tacnode point is computed using new methods and given in a different form from that obtained for a single time in previous work by Delvaux, Kuijlaars and Zhang. The form of the extended kernel is also different from that obtained for the extended tacnode kernel in another model by Adler, Ferrari and van Moerbeke. We also obtain the correlation kernel for a finite number of non-colliding Brownian motions starting at two points and ending at arbitrary points.

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