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dc.contributor.authorKuijlaars, A. B. J.
dc.contributor.authorMartínez-Finkelshtein, Andrei
dc.contributor.authorWielonsky, F.
dc.date.accessioned2012-08-01T08:31:56Z
dc.date.available2012-08-01T08:31:56Z
dc.date.issued2009
dc.identifier.urihttp://hdl.handle.net/10835/1629
dc.description.abstractWe study 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 $t = T$ at $x = 0$. In the limit $n \to \infty$, after appropriate rescaling, the paths fill out a region in the $tx$-plane that we describe explicitly. In particular, the paths initially stay away from the hard edge at $x = 0$, but at a certain critical time $t^*$ the smallest paths hit the hard edge and from then on are stuck to it. For $t \neq t^*$ we obtain the usual scaling limits from random matrix theory, namely the sine, Airy, and Bessel kernels. A key fact is that the positions of the paths at any time $t$ constitute a multiple orthogonal polynomial ensemble, corresponding to a system of two modified Bessel-type weights. As a consequence, there is a $3 \times 3$ matrix valued Riemann-Hilbert problem characterizing this model, that we analyze in the large $n$ limit using the Deift-Zhou steepest descent method. There are some novel ingredients in the Riemann-Hilbert analysis that are of independent interest.es_ES
dc.language.isoenes_ES
dc.sourceCommunications in Mathematical Physics Volume 286, Issue 1es_ES
dc.subjectProcesos de Besseles_ES
dc.subjectPolinomios ortogonaleses_ES
dc.subjectPesos de Besseles_ES
dc.subjectSquared Bessel processeses_ES
dc.subjectOrthogonal polynomialses_ES
dc.subjectModified Bessel weightses_ES
dc.titleNon-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weightses_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses_ES


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