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Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights
dc.contributor.author | Kuijlaars, A. B. J. | |
dc.contributor.author | Martínez-Finkelshtein, Andrei | |
dc.contributor.author | Wielonsky, F. | |
dc.date.accessioned | 2012-08-01T08:31:56Z | |
dc.date.available | 2012-08-01T08:31:56Z | |
dc.date.issued | 2009 | |
dc.identifier.uri | http://hdl.handle.net/10835/1629 | |
dc.description.abstract | We 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.iso | en | es_ES |
dc.source | Communications in Mathematical Physics Volume 286, Issue 1 | es_ES |
dc.subject | Procesos de Bessel | es_ES |
dc.subject | Polinomios ortogonales | es_ES |
dc.subject | Pesos de Bessel | es_ES |
dc.subject | Squared Bessel processes | es_ES |
dc.subject | Orthogonal polynomials | es_ES |
dc.subject | Modified Bessel weights | es_ES |
dc.title | Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es_ES |