Universality for the Pearcey process
(2010) Physica D: Nonlinear Phenomena — Vol. 239, n° 12, p. 924-941 (2010)
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- Abstract
- 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.
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Adler, M., Orantin, N., & Van Moerbeke, P. (2010). Universality for the Pearcey process. Physica D: Nonlinear Phenomena, 239(12), 924-941. https://doi.org/10.1016/j.physd.2010.01.005 (Original work published 2010)