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Finkelstein, A.M.1
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0346688535
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M.R. Zirnbauer, cond-mat/9903338, 1999.
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Zirnbauer, M.R.1
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0346057757
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25
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25944477474
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math-ph/9910005
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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).
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Brézin, E.1
Hikami, S.2
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26
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0347318998
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note
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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.
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28
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0347949467
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note
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This formula is used for β= 2. For technical reasons, at β= 1 and β= 4 we make use of Eq. (3.13).
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30
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0001452620
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H. Lee, L.S. Levitov, A.Yu. Yakovets, Phys. Rev. B 51 (1995) 4079; K.A. Muttalib, Y. Chen, Int. J. Mod. Phys. B 10 (1996) 1999.
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Yakovets, A.Yu.3
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37
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0347949468
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note
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N(χ,y) = φk(y) for k ∈ (0, . . . , N - 1).
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39
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0347318992
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J.-P. Fouque (Ed.), Kluwer, Dordrecht
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E. Kanzieper, V. Freilikher, in: J.-P. Fouque (Ed.), Waves in Diffuse Media, NATO ASI, Ser. C, Vol. 531, Kluwer, Dordrecht, 1999.
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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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45
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0347318995
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note
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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.
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46
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0346688505
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note
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The confinement potentials V (E) is said to be 'strong' if it increases at least as |E| at infinity.
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50
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84931537497
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