Infinite systems of non-colliding generalized meanders and Riemann-Liouville differintegrals

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dc.creatorKatori, Makoto
dc.creatorTanemura, Hideki
dc.date2005-06-10
dc.date2006-05-10
dc.date.accessioned2026-07-07T07:52:03Z
dc.date.available2026-07-07T07:52:03Z
dc.descriptionYor's generalized meander is a temporally inhomogeneous modification of the $2(ν+1)$-dimensional Bessel process with $ν> -1$, in which the inhomogeneity is indexed by $κ\in [0, 2(ν+1))$. We introduce the non-colliding particle systems of the generalized meanders and prove that they are the Pfaffian processes, in the sense that any multitime correlation function is given by a Pfaffian. In the infinite particle limit, we show that the elements of matrix kernels of the obtained infinite Pfaffian processes are generally expressed by the Riemann-Liouville differintegrals of functions comprising the Bessel functions $J_ν$ used in the fractional calculus, where orders of differintegration are determined by $ν-κ$. As special cases of the two parameters $(ν, κ)$, the present infinite systems include the quaternion determinantal processes studied by Forrester, Nagao and Honner and by Nagao, which exhibit the temporal transitions between the universality classes of random matrix theory.
dc.descriptionLaTeX, 35 pages, v3: The argument given in Section 3.2 was simplified. Minor corrections were made
dc.identifierhttps://arxiv.org/abs/math/0506187
dc.identifierhttp://arxiv.org/abs/math/0506187
dc.identifierProbab. Th. Rel. Fields 138 (2007) 113-156
dc.identifierdoi:10.1007/s00440-006-0015-4
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125739
dc.subjectProbability
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.subject60J60, 15A52, 26A33, 60G55
dc.titleInfinite systems of non-colliding generalized meanders and Riemann-Liouville differintegrals
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