Infinite systems of non-colliding Brownian particles

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

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Probability, Mathematical Physics

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http://salesiana.dossiersoluciones.com/handle/123456789/66252

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0301143
 http://arxiv.org/abs/math/0301143
 Advanced Studies in Pure Mathematics 39 ``Stochastic Analysis on Large Scale Interacting Systems", pp. 283-306 (Mathematical Society of Japan, 2004).

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