Infinite systems of noncolliding generalized meanders and Riemann-Liouville differintegrals

Makoto Katori, Hideki Tanemura

Research output: Contribution to journalArticle

20 Citations (Scopus)

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 κ ∈ [0,2(ν + 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 Jν 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.

Original languageEnglish
Pages (from-to)113-156
Number of pages44
JournalProbability Theory and Related Fields
Volume138
Issue number1-2
DOIs
Publication statusPublished - 2007 May 1
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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