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Non-colliding Brownian Motions and the Extended Tacnode Process
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-2943-7006
2013 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 319, no 1, 231-267 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2013. Vol. 319, no 1, 231-267 p.
Keyword [en]
Random-Matrix Theory, Determinantal Processes, Pearcey Process, Orthogonal Polynomials, Strong Asymptotics, Wigner Matrices, Universality, Ensembles
National Category
Physical Sciences Mathematics
URN: urn:nbn:se:kth:diva-121109DOI: 10.1007/s00220-012-1600-2ISI: 000316490100006OAI: diva2:617093
Swedish Research CouncilKnut and Alice Wallenberg Foundation, KAW2010.0063

QC 20130422

Available from: 2013-04-22 Created: 2013-04-19 Last updated: 2013-04-22Bibliographically approved

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