Vicious walk with a wall, noncolliding meanders, and chiral and Bogoliubov-deGennes random matrices
| dc.creator | Katori, Makoto | |
| dc.creator | Tanemura, Hideki | |
| dc.creator | Nagao, Taro | |
| dc.creator | Komatsuda, Naoaki | |
| dc.date | 2003-03-27 | |
| dc.date | 2003-06-24 | |
| dc.date.accessioned | 2026-07-07T02:50:25Z | |
| dc.date.available | 2026-07-07T02:50:25Z | |
| dc.description | 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 a motion of radial coordinate of the three-dimensional Brownian motion represented in the 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-deGennes Hamiltonians of the mean-field theory of superconductivity, which have the particle-hole symmetry. We report that the time evolution of the present stochastic process is fully characterized by the change of symmetry classes from the type $C$ to the type $C$I in the nonstandard classes of random matrix theory of Altland and Zirnbauer. The relation between the non-colliding 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. | |
| dc.description | REVTeX4, 16 pages, 4 figures. v2: some additions and corrections | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0303573 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0303573 | |
| dc.identifier | Phys. Rev. E 68 (2003) 021112 | |
| dc.identifier | doi:10.1103/PhysRevE.68.021112 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/21100 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Soft Condensed Matter | |
| dc.title | Vicious walk with a wall, noncolliding meanders, and chiral and Bogoliubov-deGennes random matrices | |
| dc.type | text |