The Dyson Brownian minor process

Details The Dyson Brownian minor process The Dyson Brownian minor process

2010-06-15

arxiv.org/abs/1006.2956v4

Mathematics

Probability

30 pages, 2 figures

Scientific paper

Consider an $n\times n$ Hermitean matrix valued stochastic process $\{H_t\}_{t\geq 0}$ where the matrix elements evolve according to Ornstein-Uhlenbeck processes. It is well known that the eigenvalues perform a so called Dyson Brownian motion, that is they behave as Ornstein-Uhlenbeck processes conditioned never to intersect. In this paper we study not only the eigenvalues of the full matrix, but also the eigenvalues of all the principal minors. That is, the eigenvalues of the $k\times k$ in the upper left corner of $H_t$. If you project this process to a space-like path it is a determinantal process and we compute the kernel. This kernel contains as special cases the well known GUE minor kernel, discovered by Johansson-Nordenstam and Okounkov-Reshetikhin in 2006, and the Dyson Brownian motion kernel discovered by Forrester-Nagao in 1998. In the bulk scaling limit of this kernel it is possible to recover a time-dependent generalisation of Boutillier's bead kernel.

Affiliated with

Also associated with

No associations

Rating

The Dyson Brownian minor process does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Dyson Brownian minor process, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Dyson Brownian minor process will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-104953