Vicious walks with a wall, noncolliding meanders, and chiral and Bogoliubov–de Gennes random matrices

Makoto Katori, Hideki Tanemura, Taro Nagao, Naoaki Komatsuda

研究成果: Article査読

4 被引用数 (Scopus)

抄録

Spatially and temporally inhomogeneous evolution of one-dimensional vicious walkers with wall restriction is studied. We show that its continuum version is equivalent with a noncolliding system of stochastic processes called Brownian meanders. Here the Brownian meander is a temporally inhomogeneous process introduced by Yor as a transform of the Bessel process that is the motion of radial coordinate of the three-dimensional Brownian motion represented in spherical coordinates. It is proved that the spatial distribution of vicious walkers with a wall at the origin can be described by the eigenvalue statistics of Gaussian ensembles of Bogoliubov–de Gennes Hamiltonians of the mean-field theory of superconductivity, which have a particle-hole symmetry. We report that a time evolution of the present stochastic process is fully characterized by the change of symmetry classes from type C to type [Formula presented] in the nonstandard classes of random matrix theory of Altland and Zirnbauer. The relation between the noncolliding systems of the generalized meanders of Yor, which are associated with the even-dimensional Bessel processes, and the chiral random matrix theory is also clarified.

本文言語English
ページ数1
ジャーナルPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
68
2
DOI
出版ステータスPublished - 2003 1 1
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 統計学および確率
  • 凝縮系物理学

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