2003/01/31 by Makoto Katori, Taro Nagao, Hideki Tanemura
Mathematics · Physics and Astronomy · #math.PR #math-ph #math.MP
published as Advanced Studies in Pure Mathematics 39 ``Stochastic Analysis on Large Scale Interacting Systems", pp. 283-306 (Mathematical Society of Japan, 2004). · AMS-LaTeX, 20 pages, v2: minor corrections made for publication in Advanced Studies in Pure Mathematics
arxiv created 2003/05/28 · arxiv updated 2009/11/30
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 → ∞ and the infinite time interval T → ∞. Depending on the scaling, two limit theorems are proved for the multitime correlation functions, which may define temporally inhomogeneous infinite particle systems.