"Functional central limit theorems for vicious walkers",
( with Makoto Katori)
Stoch. Stoch. Rep. 75(2003), 369-390.
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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 of nonintersecting Brownian motions,
in which we impose nonitersecting condition
in the finite time interval (0,T]
(resp. in the infinite time interval (0,))
for the first-type (resp. second-type).
The first-type is a temporally inhomogeneous diffusion, and
the second-type is a temporally homogeneous diffusion
called Dyson's model of Brownian motions.
We also study the vicious walkers with wall restriction
and prove the functional central limit theorem in the diffusion
scaling limit.
