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Infinite systems of noncolliding generalized meanders and Riemann–Liouville differintegrals
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  • Published: 06 September 2006

Infinite systems of noncolliding generalized meanders and Riemann–Liouville differintegrals

  • Makoto Katori1 &
  • Hideki Tanemura2 

Probability Theory and Related Fields volume 138, pages 113–156 (2007)Cite this article

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  • 21 Citations

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Abstract

Yor’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 \(\kappa \in [0, 2(\nu+1))\). We introduce the noncolliding particle systems of the generalized meanders and prove that they are 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.

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Author information

Authors and Affiliations

  1. Department of Physics, Faculty of Science and Engineering, Chuo University, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Makoto Katori

  2. Department of Mathematics and Informatics, Faculty of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522, Japan

    Hideki Tanemura

Authors
  1. Makoto Katori
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  2. Hideki Tanemura
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Correspondence to Makoto Katori.

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Katori, M., Tanemura, H. Infinite systems of noncolliding generalized meanders and Riemann–Liouville differintegrals. Probab. Theory Relat. Fields 138, 113–156 (2007). https://doi.org/10.1007/s00440-006-0015-4

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  • Received: 03 November 2005

  • Revised: 02 May 2006

  • Published: 06 September 2006

  • Issue Date: May 2007

  • DOI: https://doi.org/10.1007/s00440-006-0015-4

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Keywords

  • Noncolliding generalized meanders
  • Bessel processes
  • Random matrix theory
  • Fredholm Pfaffian and determinant
  • Riemann–Liouville differintegrals

Mathematics Subject Classification (2000)

  • 60J60
  • 15A52
  • 26A33
  • 60G55
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