Physical review. E, Statistical, nonlinear, andâ€¦

2002

We consider the diffusion scaling limit of the one-dimensional vicious walker model of Fisher and derive a system of nonintersecting Brownian motions. The spatial distribution of N particles isâ€¦ (More)

A system of one-dimensional Brownian motions (BMs) conditioned never to collide with each other is realized as (i) Dysonâ€™s BM model, which is a process of eigenvalues of hermitian matrixvaluedâ€¦ (More)

We consider the diffusion scaling limit of the vicious walkers, which is a model of nonintersecting random walks. We show a functional central limit theorem for the model and derive two types ofâ€¦ (More)

Physical review. E, Statistical, nonlinear, andâ€¦

2003

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 ofâ€¦ (More)

Dysonâ€™s model is a one-dimensional system of Brownian motions with long-range repulsive forces acting between any pair of particles with strength proportional to the inverse of distances withâ€¦ (More)

One-dimensional system of Brownian motions called Dysonâ€™s model is the particle system with long-range repulsive forces acting between any pair of particles, where the strength of force is Î²/2 timesâ€¦ (More)

Yorâ€™s generalized meander is a temporally inhomogeneous modification of the 2(Î½+1)-dimensional Bessel process with Î½ > âˆ’1, in which the inhomogeneity is indexed by Îº âˆˆ [0, 2(Î½ + 1)). We introduce theâ€¦ (More)

Non-colliding Brownian particles in one dimension is studied. N Brownian particles start from the origin at time 0 and then they do not collide with each other until finite time T . We derive theâ€¦ (More)

The system of one-dimensional symmetric simple random walks, in which none of walkers have met others in a given time period, is called the vicious walker model. It was introduced by Michael Fisherâ€¦ (More)

Dysonâ€™s Brownian motion model with the parameter Î² = 2, which we simply call the Dyson model in the present paper, is realized as an h-transform of the absorbing Brownian motion in a Weyl chamber ofâ€¦ (More)