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Universality in Chiral Random Matrix Theory at $\beta =1$ and $\beta =4$

Authors
  • Sener, M K
  • Verbaarschot, J J M
Publication Date
Jan 01, 1998
Identifiers
DOI: 10.1103/PhysRevLett.81.248
OAI: oai:cds.cern.ch:342376
Source
CERN Document Server
Keywords
Language
English
License
Unknown
External links

Abstract

In this paper the kernel for spectral correlation functions of the invariant chiral random matrix ensembles with real ($\beta =1$) and quaternion real ($\beta = 4$) matrix elements is expressed in terms of the kernel of the corresponding complex Hermitean random matrix ensembles ($\beta=2$). Such identities are exact in case of a Gaussian probability distribution and, under certain smoothness assumptions, they are shown to be valid asymptotically for an arbitrary finite polynomial potential. They are proved by means of a construction proposed by Brézin and Neuberger. Microscopic universality for all three chiral ensembles then follows from universal behavior for $\beta =2$ both at the hard edge (shown by Akemann, Damgaard, Magnea and Nishigaki) and at the soft edge of the spectrum (shown by Kanzieper and Freilikher).

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