"Infinite systems of non-colliding Brownian particles",
( with Makoto Katori and Taro Nagao)
Adv. Stud. Pure Math. 39(2004), 283-306.
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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 the determinantal expressions for the multitime correlation
functions using the self-dual quaternion matrices.
We consider the scaling limit of the infinite particles
$N \to \infty$ and the infinite time interval $T \to \infty$.
Depending on the scaling, two limit theorems are
proved for the multitime correlation functions, which may define
temporally inhomogeneous infinite particle systems.
