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Volumn 596, Issue 3, 2001, Pages 548-566

Random matrices and the replica method

Author keywords

Random matrix theory; Replica method; Spectral statistics

Indexed keywords


EID: 0001333957     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(00)00749-5     Document Type: Article
Times cited : (10)

References (51)
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    • We notice in passing that determinantal representation similar to Eq. (1.3) can be derived by conventional RMT tools without appealing to a σ-model mapping (see, for instance, E. Brézin, S. Hikami, math-ph/9910005).
    • Brézin, E.1    Hikami, S.2
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    • note
    • 1 (r) = sin(r)/r. This equation is a consequence of the Darboux's formula for Hankel-type determinants, and is known as a version of the discrete Toda equation.
  • 28
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    • note
    • This formula is used for β= 2. For technical reasons, at β= 1 and β= 4 we make use of Eq. (3.13).
  • 37
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    • note
    • N(χ,y) = φk(y) for k ∈ (0, . . . , N - 1).
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    • V. Freilikher, E. Kanzieper, I. Yurkevich, Phys. Rev. E 53 (1996) 2200, Phys. Rev. E 54 (1996) 210; E. Kanzieper, V. Freilikher, Phys. Rev. Lett. 78 (1997) 3806; E. Kanzieper, V. Freilikher, Philos. Mag. B 77 (1998) 1161; E. Kanzieper, V. Freilikher, Phys. Rev. E 57 (1998) 6604.
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    • V. Freilikher, E. Kanzieper, I. Yurkevich, Phys. Rev. E 53 (1996) 2200, Phys. Rev. E 54 (1996) 210; E. Kanzieper, V. Freilikher, Phys. Rev. Lett. 78 (1997) 3806; E. Kanzieper, V. Freilikher, Philos. Mag. B 77 (1998) 1161; E. Kanzieper, V. Freilikher, Phys. Rev. E 57 (1998) 6604.
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    • note
    • The identities (3.10) can be proven along the lines of Appendix A where a bit more involved cases of symplectic and orthogonal symmetries are treated.
  • 46
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    • note
    • The confinement potentials V (E) is said to be 'strong' if it increases at least as |E| at infinity.


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