The Ginibre evolution in the large-N limit
Journal Article
·
· Journal of Mathematical Physics
- Department of Mathematics, University of Warwick, Coventry CV4 7AL (United Kingdom)
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)].
- OSTI ID:
- 22306188
- Journal Information:
- Journal of Mathematical Physics, Vol. 55, Issue 6; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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