Infinite systems of noncolliding generalized meanders and Riemann-Liouville differintegrals

Makoto Katori, Hideki Tanemura

研究成果: Article査読

21 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)113-156
ページ数44
ジャーナルProbability Theory and Related Fields
138
1-2
DOI
出版ステータスPublished - 2007 5月
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 統計学および確率
  • 統計学、確率および不確実性

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