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Spatially and temporally inhomogeneous evolution of one-dimensional viciouswalkers with wall restriction is studied. We show that its continuum version isequivalent with a noncolliding system of stochastic processes called Brownianmeanders. Here the Brownian meander is a temporally inhomogeneous processintroduced by Yor as a transform of the Bessel process that is a motion ofradial coordinate of the three-dimensional Brownian motion represented in thespherical coordinates. It is proved that the spatial distribution of viciouswalkers with a wall at the origin can be described by the eigenvalue-statisticsof Gaussian ensembles of Bogoliubov-deGennes Hamiltonians of the mean-fieldtheory of superconductivity, which have the particle-hole symmetry. We reportthat the time evolution of the present stochastic process is fullycharacterized 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 andZirnbauer. The relation between the non-colliding systems of the generalizedmeanders of Yor, which are associated with the even-dimensional Besselprocesses, and the chiral random matrix theory is also clarified.Comment: REVTeX4, 16 pages, 4 figures. v2: some additions and correction

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