Tribe, Roger and Zaboronski, Oleg V. (2014) The Ginibre evolution in the large-N limit. Journal of Mathematical Physics, Volume 55 (Number 6). Article number 063304. doi:10.1063/1.4881724 ISSN 0022-2488.
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Abstract
We analyse statistics of the real eigenvalues of gl(N, R)-valued Brownian motion (the Ginibre evolution) in the limit of large N. In particular, we calculate the limiting two-time correlation function of spin variables associated with real eigenvalues of the Ginibre evolution. We also show how the formalism of spin variables can be used to compute the fixed time correlation functions of real eigenvalues discovered originally by Forrester and Nagao [“Eigenvalue statistics of the real Ginibre ensemble,” Phys. Rev. Lett.99(5), 050603 (2007)] and Borodin and Sinclair [“The Ginibre ensemble of real random matrices and its scaling limits,” Commun. Math. Phys.291(1), 177–224 (2009)].
| Item Type: | Journal Article |
|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics |
| Journal or Publication Title: | Journal of Mathematical Physics |
| Publisher: | American Institute of Physics |
| ISSN: | 0022-2488 |
| Official Date: | 20 June 2014 |
| Dates: | Date Event 20 June 2014 Published 22 August 2014 Accepted 12 August 2013 Submitted |
| Volume: | Volume 55 |
| Number: | Number 6 |
| Article Number: | Article number 063304 |
| DOI: | 10.1063/1.4881724 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | https://wrap.warwick.ac.uk/64289/ |
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