@article{AIHPA_1998__68_4_449_0, author = {Fyodorov, Yan V. and Sommers, Hans-J\"urgen and Khoruzhenko, Boris A.}, title = {Universality in the random matrix spectra in the regime of weak non-hermiticity}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {449--489}, publisher = {Gauthier-Villars}, volume = {68}, number = {4}, year = {1998}, mrnumber = {1634312}, zbl = {0907.15017}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1998__68_4_449_0/} }
TY - JOUR AU - Fyodorov, Yan V. AU - Sommers, Hans-Jürgen AU - Khoruzhenko, Boris A. TI - Universality in the random matrix spectra in the regime of weak non-hermiticity JO - Annales de l'I.H.P. Physique théorique PY - 1998 SP - 449 EP - 489 VL - 68 IS - 4 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1998__68_4_449_0/ LA - en ID - AIHPA_1998__68_4_449_0 ER -
%0 Journal Article %A Fyodorov, Yan V. %A Sommers, Hans-Jürgen %A Khoruzhenko, Boris A. %T Universality in the random matrix spectra in the regime of weak non-hermiticity %J Annales de l'I.H.P. Physique théorique %D 1998 %P 449-489 %V 68 %N 4 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPA_1998__68_4_449_0/ %G en %F AIHPA_1998__68_4_449_0
Fyodorov, Yan V.; Sommers, Hans-Jürgen; Khoruzhenko, Boris A. Universality in the random matrix spectra in the regime of weak non-hermiticity. Annales de l'I.H.P. Physique théorique, Tome 68 (1998) no. 4, pp. 449-489. http://www.numdam.org/item/AIHPA_1998__68_4_449_0/
[1] Statistical Theory of Spectra: Fluctuations, ed. by C. E. Porter Academic Press, New York, 1965.
[2] Random Matrices Academic Press, San Diego, CA, 1991. | MR | Zbl
,[3] Quantum Signature of Chaos Springer-Verlag, Berlin Heidelberg New York, 1991. | MR | Zbl
,[4] Chaos and Quantum Physics, Proceedings of the Les-Houches Summer School. Session LII, ed. by M.J. Giannoni et. al North Holland, Amsterdam, 1991, p. 91. | MR
, in[5] Mesoscopic Quantum Physics, Proceedings of the Les-Houches Summer School, Session LXI, ed. by E. Akkermans et al.
and , in[6] Rev. Mod. Phys. Vol. 69, 1997, p. 731.
,[7] Rev. Mod. Phys.
, and , to appear in[8] Proc. R. Soc. London, Ser. A, Vol. 400, 1985, p. 229. | MR | Zbl
,[9] Phys. Rev. Lett., Vol. 77, 1996, p. 1472. | Zbl
and ,[10] JETP Lett., Vol. 62, 1995, p. 76.
and ,[11] Phys. Rev. Lett., Vol. 76, 1996, p. 3947.
, , and ,[12] Phys. Rev. Lett., Vol. 61, 1988, p. 1899. | MR
, and ,[13] Phys. Rev. Lett., Vol. 63, 1989, p. 2013.
, and ,[14] Phys. Rev. Lett. 61,, 259, 1988; , and , Int. J. Bifurc. Chaos, Vol. 3, 1993, p. 279. | MR
, and ,[15] Phys. Rev. Lett., Vol. 60, 1988, p. 1895. | MR
, , and ,[16] Phys. Lett. B, Vol. 202, 1988, p. 10, and Nucl. Phys., A504, 1989, p. 562.
and ,[17] Z. Phys. B 88, 1992, p. 359; , , and , Nucl. Phys., A582, 1995, p. 223.
, , and ,[18] Phys. Rev. E52, 1995, p. 5961.
, , and ,[19] Pis'ma ZhETF, Vol. 63, 1996, p. 970, [Engl. tranls. JETP Letters, Vol. 63, 1996, p. 1026].
and ,[20] J. Math. Phys., Vol. 38, 1997, p. 1918. | MR | Zbl
and ,[21] Phys. Rev. E, 54, 1996, p. 5420; and , J. Chem .Soc. Faraday. Trans., Vol. 93, 1997, p. 847 and Phys. Rev. Lett., Vol. 78, 1997, p. 3274.
,[22] Phys. Rep., Vol. 129, 1985, p. 367. | MR
, and ,[23] Phys. Rev. E, Vol. 56, R4911, 1997; see also the related papers: , and , Phys. Rev. E, Vol. 56, R6223, 1997; , Phys. Rev. E., Vol. 56, R6237, 1997.
and ,[24] Phys. Rev. Lett., Vol. 77, 1996, p. 570 and Phys. Rev. B, Vol. 56, 1997, p. 8651.
and ,[25]
and , e-preprint cond/mat/9708071.[26] Phys. Rev. Lett., Vol. 76, 1996, p. 1461; and , Phys. Rev. Lett., Vol. 79, 1997, p. 1797.
and ,[27] Phys. Rev. Lett., Vol. 79, 1997, p. 491; Phys. Rev. B., Vol. 56, 1997, p. 9630.
,[28]
, , and , e-preprints cond-mat/9705098 and hep-th/9710103.[29] Phys. Rev. B., Vol. 56, 1997, p. 4333; and , Phys. Rev. Lett., Vol. 80, 1998, p. 2897.
, and ,[30] Nucl. Phys. B., Vol. 509, 1997, p. 599; and , e-preprint cond-mat/9710040; A. Zee e-preprint cond-mat/9711114.
and ,[31]
and , e-preprint cond-mat 9801111.[32] Phys. Rev. Lett., Vol. 76, 1996, p. 4472; , , and , Phys. Rev. Lett., Vol. 77, 1996, p. 4876; , and , Phys. Lett. B., Vol. 395, 1997, p. 293 and Phys. Rev. D., Vol. 56, 1997, p. 5140; , and , Phys. Rev. D., Vol. 56, 1997, p. 7059.
,[33] Nucl. Phys. B., Vol. 506, 1997, p. 665; and , Phys. Lett. A, Vol. 230, 1997, p. 139.
and ,[34] Pseudospectra of matrices, in Numerical Analysis, and G. A. WATSON eds. (Longman, Harlow, Essex, U.K., 1992), pp. 234-266. | MR | Zbl
,[35] Chem. Physics, Vol. 220, 1997, p. 125.
, and ,[36] J. Math. Phys., Vol. 6, 1965, p. 440. | Zbl
,[37] Phys. Rev. Lett., Vol. 67, 1991, p. 941. | MR | Zbl
and ,[38] J. Am. Math. Soc., v.7, 1994, 247; , J. Multivariate Anal., Vol. 60, 1997, p. 203. | MR | Zbl
, and ,[39] Phys. Lett. A, Vol. 169, 1992, p. 21; J. Phys. A. math. Gen., Vol. 26, 1993, p. 1179. | MR
,[40] Phys. Rev. E., Vol. 55, 1997, p. 205.
,[41] Phys. Rev. Lett., Vol. 79, 1997, p. 557. | MR | Zbl
, and ,[42] Theor. Prob. Appl., Vol. 29, 1985, p. 694 and ibid., Vol. 30, 1986, p. 677.
,[43] Ann. Prob., Vol. 25, 1997, p. 494. | Zbl
,[44] J. Phys. A. Math. Gen., Vol. 29, 1996, p. L165. | Zbl
,[45] Physics Letters A, Vol. 226, 1997, p. 46. | MR | Zbl
, and ,[46] Nucl. Phys. B., Vol. 501, 1997, p. 603. | MR | Zbl
, , and ,[47] Nucl. Phys. B, Vol. 501, 1997, p. 643 and ibid. Vol. 504, 1997, p. 579. | Zbl
and ,[48] J. Phys. A. Math. Gen., Vol. 30, 1997, p. 8635. | MR | Zbl
, , and ,[49] Ann. Math., Vol. 62, 1955, p. 548 and ibid., Vol. 67, 1958, p. 325. | Zbl
,[50] Russ. Math. Surv., Vol. 28, 1973, p. 3; see also , Annales de l'Institut Henri Poincaré. Physique Théorétique, Vol. 64, 1996, p. 325. | Numdam | Zbl
,[51] Commun. Math. Phys., Vol. 59, 1978, p. 35. | MR | Zbl
, , and ,[52] J. Stat. Phys., Vol. 79, 1995, p. 585. | MR
, and ,[53] Phys. Rev. B., Vol. 37, 1988, p. 3557. | MR
and ,[54] J. Phys. A. Math. Gen., Vol. 24, 1991, p. 2273; , , Phys. Rev. Lett., Vol. 67, 1991, p. 2049. | Zbl
, ,[55] Z. Phys. B, Vol. 99, 1995, p. 123.
and ,[56] Lett. Math.Phys., Vol. 25, 1992, p. 259; and , J. Stat. Phys., 86, 1997, p. 109.
,[57] Nucl. Phys. B., Vol. 402, 1993, p. 613. | MR | Zbl
, ,[58] Phys. Rev. Lett., Vol. 74, 1995, p. 4118.
and ,[59] Strictly speaking, the form of the correlation function of eigenvalue densities for sparse matrices was shown to be identical to that known for the corresponding Gaussian ensemble provided the average number p of non-zero elements in each row exceeds some critical value p = pl. The "threshold" value pl is nonuniversal. However, direct numerical simulations, see J. Stat. Phys., v.69, 199, 361 show that actual value is 1 < pl 2. Thus even existence of two nonvanishing elements per row already ensure, that the corresponding statistics belongs to the Gaussian universality class.
,[60] Phys. Lett., B251, 1990, p. 517; and , J. Phys. A. Math. Gen., Vol. 29, 1996, p. L555.
, and ,[61] J. Phys. A. Math. Gen., Vol. 28, 1995, L31 and J. Math. Phys., Vol. 37, 1996, p. 5033; and , Phys. Rev. E. Vol. 53, 1996, p. 1399.
, and ,[62] Phys. Lett. B., Vol. 268, 1991, p. 21. | MR
and ,[63] private communication.
and ,[64] Supersymmetry in Disorder and Chaos (Cambridge). | Zbl
,[65] Mesosocopic Quantum Physics", Les Houches Summer School, Session LXI, 1994, Edited E. AKKERMANS et al., Elsevier Science, 1995, p. 493.
, in "[66] Commun. Math. Phys., Vol. 87, 1983, p. 449. | MR | Zbl
and ,[67] J. Phys. A. Math. Gen., Vol. 26, 1993, p. 2545.
, , ,[68] The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965. | MR | Zbl
,[70] Int. J. Mod. Phys. A, Vol. 9, 1994, p. 4257. | Zbl
, , and ,[71] Int. J. Mod. Phys. A, Vol. 11, 1997, p. 941. | MR | Zbl
and ,[72] Orthogonal polynomials, 4th ed. (AMS, Providence, 1975), p. 380. | MR
,[73] Table of Integrals, Series, and Products Academic Press, N.Y. 1980.
, ,[74] Phys. Rev. E, Vol. 56, 1997, p. 2481.
, , , and ,