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Communications in Mathematical Physics

, Volume 319, Issue 1, pp 231–267 | Cite as

Non-colliding Brownian Motions and the Extended Tacnode Process

  • Kurt JohanssonEmail author
Article

Abstract

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.

Keywords

Brownian Motion Dominate Convergence Theorem Random Matrix Theory Left Half Plane Fredholm Determinant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsKTH Royal Institute of TechnologyStockholmSweden

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