The integral equations for the average stochastic scattering matrix

Girko, V. L.; Ezhov, S.N.; Plujko, V. A.

doi:10.1515/rose.1993.1.2.161

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Cited by 2 publications

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“…The problem is to find the limits of the expressions E5« and E[(5 -E5)y (5 -ES)p|Cn] as Ν ->> oo, Λ -* oo, where c n is some sequence of normalizing values. In [52,53] the limit theorems for these expressions were proved under the condition that…”

Section: S = B = F(ie -Hq-v + ^F T F)-1 F T mentioning

confidence: 99%

Numerical and Monte Carlo verification of V-distribution

Dias¹,

Girko²

1998

Random Operators and Stochastic Equations

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Section: S = B = F(ie -Hq-v + ^F T F)-1 F T mentioning

confidence: 99%

Numerical and Monte Carlo verification of V-distribution

Dias¹,

Girko²

1998

Random Operators and Stochastic Equations

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“…Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering. Random matrix approach for systems with broken time-reversal invariance [60][61][65][66][67]. For data of the complete spin and parity, the symmetric and unitary matrix of scattering can be written in the form: -where U is a unitary matrix of dimension TV χ TV; V and F are the real random matrices of dimensions Λ χ Λ and TV χ Λ with the elements Vij and 7^, respectively, / is the identity matrix of dimension TV χ TV, the matrices H 0 and V are nonrandom, and HQ, V, F do not depend on the energy ε.…”

mentioning

confidence: 99%

The V-density of eigenvalues of non symmetric random matrices and rigorous proof of the strong Circular law

Girko¹

1997

Random Operators and Stochastic Equations

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We review some results obtained in series of papers on non Hermitian random matrices in some problems of spin glasses and neural nets. We present new theory of such matrices on the basis of the V-transform of normalized spectral function (n.s.f.) i^n(^,2/) of the eigenvalues of non symmetric matrix Ξ with n.s.f. /x n (x,r) of the eigenvalues of the Hermitian G-matrix (Ξ -τ/) (Ξ -τ/)*, τ = t + is : 7 q φ. Ο, and the modified V^-transform:where ε > 0. This article discusses methodological approach which allows one to obtain rigorous proof of the strong Circular law and to describe the region where the eigenvalues of large non Hermitian random matrices are distributed.

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The integral equations for the average stochastic scattering matrix

Cited by 2 publications

References 0 publications

Numerical and Monte Carlo verification of V-distribution

Numerical and Monte Carlo verification of V-distribution

The V-density of eigenvalues of non symmetric random matrices and rigorous proof of the strong Circular law

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