Consecutive minors for Dyson's Brownian motions
(2014) Stochastic Processes and Their Applications — Vol. 124, n° 6, p. 2023-2051 (2014)
Files
pdfdocument.pdf
Restricted Access - Adobe PDF
- 328.11 KB
Details
- Authors
- Abstract
- In 1962, Dyson (1962) introduced dynamics in random matrix models, in particular into GUE (also for β=1 and 4), by letting the entries evolve according to independent Ornstein-Uhlenbeck processes. Dyson shows the spectral points of the matrix evolve according to non-intersecting Brownian motions. The present paper shows that the interlacing spectra of two consecutive principal minors form a Markov process (diffusion) as well. This diffusion consists of two sets of Dyson non-intersecting Brownian motions, with a specific interaction respecting the interlacing. This is revealed in the form of the generator, the transition probability and the invariant measure, which are provided here; this is done in all cases: β=1,2,4. It is also shown that the spectra of three consecutive minors ceases to be Markovian for β=2,4.© 2014 Elsevier B.V. All rights reserved.
- Affiliations
Citations
Adler, M., Van Moerbeke, P., & Nordenstam, E. (2014). Consecutive minors for Dyson’s Brownian motions. Stochastic Processes and Their Applications, 124(6), 2023-2051. https://doi.org/10.1016/j.spa.2014.01.008 (Original work published 2014)