Non-colliding system of Brownian particles as Pfaffian process

Abstract

In the paper [7] we studied the temporally inhomogeneous system of non-colliding Brownian motions and proved that multi-time correlation functions are generally given by the quaternion determinants in the sense of Dyson and Mehta. In this report we give another proof of the equivalent statement using Fredholm determinant and Fredholm pfaffian, and claim that the present system is a typical example of pfaffian processes.

LaTeX, 14 pages, 1 figure

References in corpus (8)

• Eynard-Mehta theorem, Schur process, and their pfaffian analogs
• Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems
• Correlation functions for symmetrized increasing subsequences
• Fluctuations of a one-dimensional polynuclear growth model in a half space
• Scaling limit of vicious walks and two-matrix model
• Dynamical Correlations among Vicious Random Walkers
• Functional central limit theorems for vicious walkers
• Infinite systems of non-colliding generalized meanders and Riemann-Liouville differintegrals