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dc.contributor.authorKuijlaars, A. B. J.
dc.contributor.authorMartínez-Finkelshtein, Andrei
dc.contributor.authorWielonsky, F.
dc.date.accessioned2012-07-12T11:52:40Z
dc.date.available2012-07-12T11:52:40Z
dc.date.issued2011
dc.identifier.urihttp://hdl.handle.net/10835/1590
dc.description.abstractWe consider the double scaling limit for a model of n non-intersecting squared Bessel processes in the confluent case: all paths start at time t = 0 at the same positive value x = a, remain positive, and are conditioned to end at time t = 1 at x = 0. After appropriate rescaling, the paths fill a region in the tx–plane as n → ∞ that intersects the hard edge at x = 0 at a critical time t = t *. In a previous paper, the scaling limits for the positions of the paths at time t ≠ t * were shown to be the usual scaling limits from random matrix theory. Here, we describe the limit as n → ∞ of the correlation kernel at critical time t * and in the double scaling regime. We derive an integral representation for the limit kernel which bears some connections with the Pearcey kernel. The analysis is based on the study of a 3 × 3 matrix valued Riemann-Hilbert problem by the Deift-Zhou steepest descent method. The main ingredient is the construction of a local parametrix at the origin, out of the solutions of a particular third-order linear differential equation, and its matching with a global parametrix.es_ES
dc.language.isoenes_ES
dc.sourceCommunications in Mathematical Physics Vol. 308, Number 1 (2011)es_ES
dc.subjectDouble scalinges_ES
dc.subjectModel of nes_ES
dc.subjectSquared Bessel processeses_ES
dc.subjectDoble escalaes_ES
dc.subjectModelo de nes_ES
dc.subjectProcesos cuadrados de Besseles_ES
dc.titleNon-intersecting squared Bessel paths: critical time and double scaling limites_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses_ES


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