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VOL. 39 | 2004 Infinite Systems of Non-Colliding Brownian Particles
Makoto Katori, Taro Nagao, Hideki Tanemura

Abstract

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.

Information

Published: 1 January 2004
First available in Project Euclid: 1 January 2019

zbMATH: 1074.82020
MathSciNet: MR2073337

Digital Object Identifier: 10.2969/aspm/03910283