Universality for the Pearcey process

PHYSICA D-NONLINEAR PHENOMENA

卷:239

Article

Adler, Mark²  Orantin, Nicolas³  van Moerbeke, Pierre^1,2 

[1] Univ Louvain, Dept Math, B-1348 Louvain, Belgium

[2] Brandeis Univ, Dept Math, Waltham, MA 02454 USA

[3] CERN, Div Theory, CH-1211 Geneva 23, Switzerland

关键词: Non-intersecting Brownian motions;    Pearcey distribution;    Matrix models;    Random Hermitian ensembles;    Multi-component KP equation;    Virasoro constraints;   

DOI  :  10.1016/j.physd.2010.01.005

来源: Elsevier

【 摘 要 】

Consider non-intersecting Brownian motions on the line leaving from the origin and forced to two arbitrary points. Letting the number of Brownian particles tend to infinity, and upon rescaling, there is a point of bifurcation, where the support of the density of particles goes from one interval to two intervals. In this paper, we show that at that very point of bifurcation a cusp appears, near which the Brownian paths fluctuate like the Pearcey process. This is a universality result within this class of problems. Tracy and Widom obtained such a result in the symmetric case, when the two target points are symmetric with regard to the origin. This asymmetry enabled us to improve considerably a result concerning the non-linear partial differential equations governing the transition probabilities for the Pearcey process, obtained by Adler and van Moerbeke. (c) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free