The Pearcey Process
| dc.creator | Tracy, Craig A. | |
| dc.creator | Widom, Harold | |
| dc.date | 2004-12-01 | |
| dc.date | 2005-09-21 | |
| dc.date.accessioned | 2026-07-07T06:26:49Z | |
| dc.date.available | 2026-07-07T06:26:49Z | |
| dc.description | The extended Airy kernel describes the space-time correlation functions for the Airy process, which is the limiting process for a polynuclear growth model. The Airy functions themselves are given by integrals in which the exponents have a cubic singularity, arising from the coalescence of two saddle points in an asymptotic analysis. Pearcey functions are given by integrals in which the exponents have a quartic singularity, arising from the coalescence of three saddle points. A corresponding Pearcey kernel appears in a random matrix model and a Brownian motion model for a fixed time. This paper derives an extended Pearcey kernel by scaling the Brownian motion model at several times, and a system of partial differential equations whose solution determines associated distribution functions. We expect there to be a limiting nonstationary process consisting of infinitely many paths, which we call the Pearcey process, whose space-time correlation functions are expressible in terms of this extended kernel. | |
| dc.description | LaTeX 24 pages. Version 3 has an improved exposition and corrects a minor error | |
| dc.identifier | https://arxiv.org/abs/math/0412005 | |
| dc.identifier | http://arxiv.org/abs/math/0412005 | |
| dc.identifier | Commun. Math. Phys. 263, 381-400 (2006) | |
| dc.identifier | doi:10.1007/s00220-005-1506-3 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97225 | |
| dc.subject | Probability | |
| dc.title | The Pearcey Process | |
| dc.type | text |