Infinite systems of non-colliding Brownian particles

Details Infinite systems of non-colliding Brownian particles Infinite systems of non-colliding Brownian particles

2003-01-14

arxiv.org/abs/math/0301143v2

Advanced Studies in Pure Mathematics 39 ``Stochastic Analysis on Large Scale Interacting Systems", pp. 283-306 (Mathematical S

Mathematics

Probability

AMS-LaTeX, 20 pages, v2: minor corrections made for publication in Advanced Studies in Pure Mathematics

Scientific paper

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.

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