Artículos de revistas
Numerical And Monte Carlo Verification Of V-distribution
Registro en:
Random Operators And Stochastic Equations. , v. 6, n. 2, p. 201 - 212, 1998.
9266364
2-s2.0-84868015059
Autor
Dias R.
Girko V.
Institución
Resumen
Tt is shown that V-distribution is a valid probability density for all values of parameters and approximates the empirical density of eigenvalues of certain random non symmetrical matrices. © 1998 VSP. 6 2 201 212 Porter, C.E., (1965) Statistical Theories of Spectra: Fluctuations, Collection of Re Prints and Original Papers, , Academic Press, New York Dyson, F.J., The dynamics of disordered linear chain (1953) Phys. Rev., 92 (6), pp. 1331-1338 Dyson, F.J., A Brownian-motion model for the eigenvalue of a random matrix (1962) Math. Phys., 3 (6), pp. 31-60 Dyson, F.J., Correlations between eigenvalues of a random matrix (1970) Commun. Math. Phys., 19, pp. 235-250 Ginibre, I., Statistical ensembles of complex, quaternion, and real matrices (1965) J. Math. Phys., 6, pp. 440-449 Mehta, M.L., (1967) Random Matrices and the Statistical Theory of Energy Levels, , Academic Press, New York, London Evangelou, S.N., Katsanos, D.E., Energy level statistics in disordered metals with an anderson transition (1996) Jornal of Statistical Physics, 85 (5-6), pp. 525-550 Schmidt, H., Disordered one-dimensional crystals (1957) Phys. Rev., 105 (2), pp. 425-441 Lifshits, I.M., On the structure of the energy spectrum and quantum state of disordered condenser systems (1965) Sov. Fiz. Usp., 7, pp. 549-573. , in Russian Wigner, E.P., Statistical properties of real symmetric matrices with many dimensions (1957) Can. Math. Proc., pp. 174-198 Wigner, E.P., On the distribution of the roots of certain symmetric matrices (1958) Ann. Math., 67 (2), pp. 325-327 Wigner, E.P., Random matrices in physics (1967) SIAM Rev., 9 (1), pp. 1-23 Zakrewski, J., Dupret, K., Delande, D., Wigner or non-wigner: That is the question (1995) Proceedings of the XXXIst Winter School of Theoretical Physics "chaos-The Interplay between Stochastic and Deterministic Behavior", pp. 559-564. , Springer Girko, V.L., Spectral theory of random matrices (1985) Russian Math. Surveys, 40 (1), pp. 77-120 Kuz, M., Lewentein, M., Haake, F., Density of eigenvalues of random band matrices (1991) Phya. Rev. A, 44 (5), pp. 2800-2808 Girko, V.L., Preston, N., Numerical and monte carlo verification of the first spacing law (1996) Random Operators and Stochastic Equations, 4 (4), pp. 303-314 De Monvel, B., Pastur, L., Shcerbina, M., On the statistical mechanics approach in the random matrix theory: Integrated density of states (1995) Stat. Phys., 79 (3-4), pp. 585-613 De Monvel, B., Khorunzhy, A., Vasilchuk, V., Limiting eigenvalue distribution of random matrices with correlated entries (1996) Markov Processes Relat. Fields, 2, pp. 607-636 Brody, T.A., Flores, J., French, J., Mello, P.A., Pandey, A., Wong, S., Randommatrix physics: Spectrum and strength fluctuation (1981) Rev. Modern Phys., 58 (3), pp. 385-479 Camarda, H.S., Georgopulos, P.P., Statistical behaviour of atomic energy levels: Aqreement with random matrix theory (1983) Phys. Rev. Letters, 50, pp. 492-495 Casati, G., Molinari, G.L., Izrailev, F.M., Scaling properties of band random matrices (1980) Phys. Rev. Lett., 64, pp. 1851-1854 Constantinescu, F., Felder, G.M., Gawedzki, K., Kupiainen, A., Analyticity of density of states (1987) Stat. Phys., 48 (3), pp. 365-391 Girko, V.L., Casati, G., Molinari, L., Equation for limit spectral functions of band random matrices (1993) Random Oper. Stock. Eqs., 1 (1), pp. 1-6 Pastur, L.A., The spectra of random selfadjoint operators (1973) Russian Math. Surveys, 28 (1), pp. 1-67 Girko, V.L., Casati, G., Generalized Wigner law for band random matrices (1993) Random Oper. Stock. Eqs., 1, p. 1 Girko, V.L., Casati, G., Limit theorems for band random matrices whose entries have bounded variances (1993) Random Oper. Stock. Eqs., 1 (2), pp. 181-191 Girko, V.L., Kirsch, W., Kutzelnigg, A., Necessary and sufficient conditions for the semicircle law (1994) Random Oper. Stock. Eqs., 2 (2), pp. 195-202 Opperman, R., Wegner, F., Disordered System with N Orbitals per Site: N - 1 Expansion (1979) Z. Phys., 34, pp. 327-348 Khorunzhy, A., Pastur, L., Limits of infinite interaction radius, dimensionality and the number of components for random operators with off-diagonal randomness (1993) Commun. Math. Phys., 153, pp. 605-646 Khorunzhy, A., Khoruzhenko, B., Pastur, L., On the ln corrections to the green functions of random matrices with independent entries. of physics a (1995) Mathematical and General., 28, pp. L31-L35 Khorunzhy, A., Khoruzhenko, B., Pastur, L., Asymptotic properties of large random matrices with independent entries (1996) Math. Phys., 37 (10), pp. 5033-5060 Marchenko, V.A., Pastur, L.A., Distribution of the eigenvalues in certain sets of random matrices (1967) Mat. Sb., 1, pp. 457-483. , in Russian Pastur, L.A., On the universality of the level spacing distribution for some ensemble of random matrices (1992) Lett. Math. Phys., 25, pp. 259-265 Pastur, L.A., Shcherbina, M., Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles (1997) Stat. Phys., 86, pp. 109-147 Pastur, L.A., Figotin, A., (1992) Spectra of Random and Almost Periodic Operators, , Springer Verlag Schafer, L., Wegner, F., Disordered System with N Orbitals per Site: Lagrange Formulation (1980) Z. Phys., 38, pp. 113-126 Sommers, H.J., Crisanti, A., Sompolinsky, H., Stein, Y., Spectrum of large random asymmetric matrices (1988) Phys. Rev. Lett., 60, pp. 1895-1898 Khorunzenko, B., Large-TV eigenvalue distribution of randomly perturbed asymetric matrices (1996) Phys. A: Math. Gen., 29, pp. L165-L169 Fyodorov, Y.V., Khoruzenko, H.J.B., Sommers, Almost-Hermitian random matrices: Eigenvalue density in the complex plane (1997) Physics Letters A, 226 (1-2), pp. 46-51 Haake, F., (1991) Quantum Signatures of Chaos, , Springer Verlag, Heidelberg Izrailev, F.M., Simple models of quantum chaos: Spectrum and eigenfunctions (1990) Phus. Report., 196 (5-6), pp. 299-392 Guhr, T., Transitions toward quantum chaos: With supersymmetry from Poisson to Gauss (1996) Annals of Physics, 250, pp. 145-192 Bessis, D., Itzykson, C., Zuber, J., Quantum field theory techniques in graphical enumeration (1980) Adv. Appl Math., 1, pp. 109-157 Brezin, E., Itzykson, C., Paris, G., Zuber, I., Planar diagrams (1978) Commun. Math. Phys., 59, pp. 35-51 Brezin, E., Zee, A., Universality of the correlations between eigenvalues of large random matrices (1993) Nucl Phys. B., 402, pp. 613-627 Demetrefi, K., Two-dimensional quantum gravity, matrix models and string theory (1993) Int. J. Mod. Phys. A., 8, pp. 1185-1244 Franchesco, P.D., Ginsparg, P., Zinn-Justin, J., 2D gravity and random matrices (1995) Phys. Rep., 254 (1) Fyodorov, Y.V., Alexander, D.M., Scaling properties of localization in random band matrices: A s-model approach (1991) Phys. Rev. Lett., 67, pp. 2405-2409 Fyodorov, Y.V., Sommers, H.L., Statistics of resonance poles, phase shifts ant time delays in quantum chaotic scattering: Random matrix approach for systems with broken time-reversal invariance (1997) Journal of Mathematical Physics, 38 (4), pp. 1918-1981 Bogomolny, E., Bohigas, O., Leboeuf, P., Quantum chaotic dynamics and random polynomials (1996) Journal of Statistical Physics, 85 (5-6), pp. 639-679 Fernandez, R., Frölich, J., Sokal, A., (1992) Random Walks Critical Phenomena and Tnviality in the Quantum Field Theory, , Springer Verlag, Heidelberg Girko, V.L., Ezhov, S.N., Pluyko, V.A., Integral equations for average scattering matrix (1988) Ukr. Fiz. Zh., 33 (10), p. 1451. , in Russian Girko, V.L., Ezhov, S.N., Pluyko, V.A., The integral equations for the average stochastic scattering matrix (1993) Random Oper. Stoch. Eqs., 1 (2), pp. 161-170 Girko, V.L., Olhovsky, V.S., Chinarov, V.A., To the theory of fluctuation of unitary 5-matrix for nuclear reactions (1984) Izv. Akad. Nauk SSSR, 48 (1), pp. 166-171. , in Russian Aizenman, M., Lebowitz, J.L., Ruelle, D., Some rigorous results on the sherington-kirkpatrick spin glass model (1987) Commun. Math. Phys., 112, pp. 3-20 Hertz, J.A., Statistical dynamics of learning, in: Lecture Notes in Physics (1990) Statistical Mechanics of Neural Networks, Proceedings, Sitges, , Ed. Luis Garrido, Barcelona, Spain, Springer-Velag Crisanti, A., Sompolinsky, H., Dynamics of spin systems with randomly asymmetric bonds: Langevin dynamics and a spherical model (1987) Phys. Rev. A., 36 (10), pp. 4922-4939 Lehmann, N., Sommers, H.J., Eigenvalue statistics of random real matrices (1991) Phys. Rev. Lett., 67 (8), pp. 941-944 Girko, V.L., (1975) Random Matrices, , Kiev, Published by Kiev University, in Russian Girko, V.L., V-Transform (1982) Reports AN USSR, Series of Mathematics and Mechanics, 3, pp. 5-6 Girko, V.L., On the circle law (1983) Theory of Probability and Mathematical Statistics, 28, pp. 15-23 Girko, V.L., The Circle law (1984) Theory of Probabilities and Their Applications, 29 (4), pp. 669-679 Girko, V.L., Regularized V-transform (1984) Theory of Probability and Its Applications, 29 (2), pp. 416-417 Girko, V.L., (1985) The Elliptic Law, R.eports of the Fourth Vilnius Conference on the Theory of Probability and Mathematical Statistics, pp. 171-173. , Vilnius Girko, V.L., The Elliptic law (1985) Doclady AN USSR, Ser. Matematika i Mehanika, 1, pp. 3-7 Girko, V.L., The Elliptic law (1985) Theory of Probability and Their Applications, 30 (4), pp. 640-651 Girko, V.L., The elliptic law and elements of G-analysis (1987) Proceedings of the Fourth Vilnius Conference, 1, pp. 489-509. , VNU Science Press BV Girko, V.L., (1990) Theory of Random Determinants, , Kluwer Academic Publishers Girko, V.L., Canonical spectral equation for singular spectral functions of random matrices (1993) Russian Math. Surveys., 48 (3), pp. 163-180 Girko, V.L., The circular law: Ten years later (1994) Random Oper, and Stock. Equ., 2 (3), pp. 235-277 Girko, V.L., The Elliptic Law: Ten Years Later i (1995) Random Operators and Stochastic Equations, 3 (3), pp. 257-302 Girko, V.L., The Elliptic Law: Ten Years Later II (1995) Random Operators and Stochastic Equations, 3 (4), pp. 377-398 Girko, V.L., (1996) Theory of Linear Algebraic Equations with Random Coefficients, p. 320. , Allerton Press, Inc. New York Girko, V.L., Strong circular law (1997) Random Operators and Stochastic Equations, 5 (2), pp. 173-196 Girko, V.L., Strong Elliptic law (1997) Random Operators and Stochastic Equations, 5 (3), pp. 269-302 Rodgers, G.L., Bray, A.J., Density of states of a sparse random matrices (1988) Phys. Rev., 537, pp. 3557-3762 Rodgers, G., Dominicis, C., Density of states of a sparse random matrices (1990) Phys. A, 23, pp. 1567-1573 Khorunzhy, A., Rodgers, G.L., Eigenvalue distribution of large dilute random matrices (1997) J. Math. Phys., 38 (6), pp. 3300-3320 Sompolinsky, H., Neural networks with non-linear synapces and static noise (1986) Phys. Rev. A, 34, pp. 2571-2574 Guhr, T., Wettig, T., An Itzykson-Zuber-like integral and diffusion for complex ordinary and supermatrices,.7 (1996) Math. Phys., 37 (12), pp. 6395-6413 Itzykson, C., Zuber, J.B., The planar approximation II (1980) Math. Phys., 21 (3), pp. 411-421 Girko, V.L., The V-density of eigenvalues of non symmetric random matrices and rigorous proof of the strong Circular law (1997) Random Operators and Stochastic Equations, 5 (4), pp. 371-406