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References[1] L. AAGARD; Thenon-microstates free entropy dimension of DT-operators. Preprint Syddansk Universitet (2003) [2] G. ANDERSON, O. ZEITOUNI; A clt for a band matrix model, preprint (2004) [3] A. APTEKAREV, P. BLEHER, A. KUIJLAARS ; Large n limit of Gaussian matrices with external source, part II. http://arxiv.org/abs/math-ph/0408041 [4] Z.D. BAI; Convergence rate of expected spectral distributions of large random matrices I. Wigner matrices Ann. Probab. 21 : 625–648 (1993) MR1217559 [5] Z.D. BAI; Methodologies in spectral analysis of large dimensional random matrices: a review, Statistica Sinica 9, No 3: 611–661 (1999) MR1711663 [6] Z.D. BAI, J.F. YAO; On the convergence of the spectral empirical process of Wigner matrices, preprint (2004) [7] Z.D. BAI, Y.Q. YIN; Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix. Ann. Probab. 21:1275–1294 (1993) MR1235416 [8] J.BAIK, P. DEIFT, K. JOHANSSON; On the distribution of the length of the longest increasing subsequence of random perturbations J. Amer. Math. Soc. 12: 1119–1178 (1999) MR1682248 [9] G. BEN AROUS, A. DEMBO, A. GUIONNET, Aging of spherical spin glasses Prob. Th. Rel. Fields 120: 1–67 (2001) MR1856194 [10] G. BEN AROUS, A. GUIONNET, Large deviations for Wigner’s law and Voiculescu’s non-commutative entropy, Prob. Th. Rel. Fields 108: 517–542 (1997). MR1465640 [11] G. BEN AROUS, O. ZEITOUNI; Large deviations from the circular law ESAIM Probab. Statist. 2: 123–134 (1998) MR1660943 [12] F.A. BEREZIN; Some remarks on the Wigner distribution, Teo. Mat. Fiz. 17, N. 3: 1163–1171 (English) (1973) MR468719 [13] H. BERCOVICI and D. VOICULESCU; Free convolution of measures with unbounded support. Indiana Univ. Math. J. 42: 733–773 (1993) MR1254116 [14] M. BERTOLA; Second and third observables of the two-matrix model. http://arxiv.org/abs/hep-th/0309192 [15] P.BIANE On the Free convolution with a Semi-circular distribution Indiana Univ. Math. J. 46 : 705–718 (1997) MR1488333 [16] P. BIANE; Calcul stochastique non commutatif, Ecole d’été de St Flour XXIII 1608: 1–96 (1993) [17] P. BIANE, R. SPEICHER; Stochastic calculus with respect to free brownian motion and analysis on Wigner space, Prob. Th. Rel. Fields, 112: 373–409 (1998) MR1660906 [18] P. BIANE, M. CAPITAINE, A. GUIONNET; Large deviation bounds for the law of the trajectories of the Hermitian Brownian motion. Invent. Math.152: 433–459 (2003) MR1975007 [19] P. BLEHER, A. KUIJLAARS ; Large n limit of Gaussian matrices with external source, part I. http://arxiv.org/abs/math-ph/0402042 [20] E. BOLTHAUSEN; Laplace approximations for sums of independent random vectors Probab. Theory Relat. Fields 72 :305–318 (1986) MR836280 [21] D.V. BOULATOV, V. KAZAKOV ; The Ising model on a random planar lattice: the structure of the phase transition and the exact critical exponents Phys. Lett. B 186: 379–384 (1987) MR882684 [22] M. BOUSQUET MELOU, G. SCHAEFFER; The degree distribution in bipartite planar maps: applications to the Ising model http://front.math.ucdavis.edu/math.CO/0211070 [23] A. BOUTET DE MONVEL, A. KHORUNZHI; On universality of the smoothed eigenvalue density of large random matrices J. Phys. A 32: 413–417 (1999) MR1733840 [24] A. BOUTET DE MONVEL, A. KHORUNZHI; On the norm and eigenvalue distribution of large random matrices. Ann. Probab. 27: 913–944 (1999) MR1698983 [25] A. BOUTET DE MONVEL, M. SHCHERBINA; On the norm of random matrices, Mat. Zametki57: 688–698 (1995) MR1347371 [26] Y. BRENIER, Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations Comm. Pure. Appl. Math. 52: 411–452 (1999) MR1658919 [27] N. BROWN; Finite free entropy and free group factors http://front.math.ucdavis.edu/math.OA/0403294 [28] T. CABANAL-DUVILLARD; Fluctuations de la loi spectrale des grandes matrices aléatoires, Ann. Inst. H. Poincaré 37: 373–402 (2001) MR1831988 [29] T. CABANAL-DUVILLARD, A. GUIONNET; Large deviations upper bounds and non commutative entropies for some matrices ensembles, Annals Probab. 29 : 1205–1261 (2001) MR1872742 [30] T. CABANAL-DUVILLARD, A. GUIONNET; Discussions around non-commutative entropies, Adv. Math. 174: 167–226 (2003) MR1963692 [31] G. CASATI, V. GIRKO; Generalized Wigner law for band random matrices, Random Oper. Stochastic Equations 1: 279–286 (1993) MR1254409 [32] S. CHADHA, G. MADHOUX, M. L. MEHTA; A method of integration over matrix variables II, J. Phys. A. 14: 579–586 (1981) MR605258 [33] T. CHIYONOBU; A limit formula for a class of Gibbs measures with long range pair interactions J. Math. Sci. Univ. Tokyo7;463–486 (2000) MR1792737 [34] B. COLLINS; Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral, and free probability Int. Math. Res. Not. 17: 953–982 (2003) [35] A. CONNES, D. SHLYAKHTENKO; L2-Homology for von Neumann Algebras http://front.math.ucdavis.edu/math.OA/0309343 [36] M. CORAM , P. DIACONIS; New test of the correspondence between unitary eigenvalues and the zeros of Riemann’s zeta function, Preprint Feb 2000, Stanford University [37] P. DIACONIS , M. SHAHSHAHANI; On the eigenvalues of random matrices. Jour. Appl. Probab. 31 A: 49–62 (1994) MR1274717 [38] P. DIACONIS , A. GANGOLLI; Rectangular arrays with fixed margins IMA Vol. Math. Appl. 72 : 15–41 (1995) [39] A. DEMBO , F. COMETS; Large deviations for random matrices and random graphs, preprint (2004) [40] A. DEMBO , A. VERSHIK , O. ZEITOUNI; Large deviations for integer paprtitions Markov Proc. Rel. Fields 6: 147–179 (2000) MR1778750 [41] A. DEMBO, O. ZEITOUNI; Large deviations techniques and applications, second edition, Springer (1998). MR1619036 [42] A. DEMBO, A. GUIONNET, O. ZEITOUNI; Moderate Deviations for the Spectral Measure of Random Matrices Ann. Inst. H. Poincaré 39: 1013–1042 (2003) MR2010395 [43] J.D. DEUSCHEL, D. STROOCK; large deviations Pure Appl. Math. 137 Academic Press (1989) [44] K. DYKEMA, U. HAAGERUP; Invariant subspaces of the quasinilpotent DT-operator J. Funct. Anal. 209: 332–366 (2004) MR2044226 [45] F.J. DYSON; A Brownian motion model for the eigenvalues of a random matrix J. Mathematical Phys. 3: 1191–1198 (1962) MR148397 [46] N.M. ERCOLANI, K.D.T-R McLAUGHLIN; Asymptotics of the partition function for random matrices via Riemann-Hilbert techniques, and applications to graphical enumeration. Int. Math. res. Notes 47 : 755–820 (2003) [47] B. EYNARD; Eigenvalue distribution of large random matrices, from one matrix to several coupled matrices, Nuclear Phys. B. 506: 633–664 (1997). MR1488592
[48] B. EYNARD; Random matrices,
[49] B. EYNARD; Master loop equations, free energy and correlations for the chain of matrices. http://arxiv.org/abs/hep-th/0309036 [50] B. EYNARD, A. KOKOTOV, D. KOROTKIN; 1∕N2 correction to free energy in hermitian two-matrix model , http://arxiv.org/abs/hep-th/0401166 [51] H. FOLLMER;An entropy approach to the time reversal of diffusion processes Lect. Notes in control and inform. Sci. 69: 156–163 (1984) [52] J. FONTBONA; Uniqueness for a weak non linear evolution equation and large deviations for diffusing particles with electrostatic repulsion Stoch. Proc. Appl. 112: 119–144 (2004) MR2062570 [53] P. FORRESTER http://www.ms.unimelb.edu.au/~matpjf/matpjf.html [54] Y. FYODOROV, H. SOMMERS, B. KHORUZHENKO; Universality in the random matrix spectra in the regime of weak non-Hermiticity. Classical and quantum chaos. Ann. Inst. Poincare. Phys. Theor. 68: 449–489 (1998) MR1634312 [55] D. GABORIAU; Invariants ℓ2 de relations d’équivalences et de grroupes Publ. Math. Inst. Hautes. Études Sci. 95: 93–150(2002) [56] L. GE; Applications of free entropy to finite von Neumann algebras, Amer. J. Math. 119: 467–485(1997) MR1439556 [57] L. GE; Applications of free entropy to finite von Neumann algebras II,Annals of Math. 147: 143–157(1998) MR1609522 [58] GIRKO, V.; Theory of random determinants , Kluwer (1990) [59] T. GUHR, A. MUELLER-GROELING, H. A. WEIDENMULLER; random matrix theory in quantum Physics : Common concepts arXiv:cond-mat/9707301(1997) [60] A. GUIONNET; Large deviation upper bounds and central limit theorems for band matrices, Ann. Inst. H. Poincaré Probab. Statist 38 : 341–384 (2002) MR1899457 [61] A. GUIONNET; First order asymptotic of matrix integrals; a rigorous approach toward the understanding of matrix models, Comm.Math.Phys 244: 527–569 (2004) MR2034487 [62] A. GUIONNET , M. MAIDA; Character expansion method for the first order asymptotics of a matrix integral. http://front.math.ucdavis.edu/math.PR/0401229 [63] A. GUIONNET , M. MAIDA; An asymptotic log-Fourier interpretation of the R-transform. http://front.math.ucdavis.edu/math.PR/0406121 [64] A. GUIONNET, O. ZEITOUNI; Concentration of the spectral measure for large matrices, Electron. Comm. Probab. 5: 119–136 (2000) MR1781846 [65] A. GUIONNET, O. ZEITOUNI; Large deviations asymptotics for spherical integrals, Jour. Funct. Anal. 188: 461–515 (2001) [66] A. GUIONNET, O. ZEITOUNI; Addendum to Large deviations asymptotics for spherical integrals, To appear in Jour. Funct. Anal. (2004) [67] F. HIAI; Free analog of pressure and its Legendre transform http://front.math.ucdavis.edu/math.OA/0403210 [68] J. HARER, D. ZAGIER; The Euler caracteristic of the moduli space of curves Invent. Math. 85: 457–485(1986) MR848681 [69] U. HAAGERUP, S. THORBJORNSEN; A new application of Random matrices : Ext(Cred*(F2)) is not a group. http://fr.arxiv.org/pdf/math.OA/0212265. [70] S. HANLY, D. TSE; Linear multiuser receivers: effective interference, effective bandwidth and user capacity. IEEE Trans. Inform. Theory 45 , no. 2, 641–657 (1999) MR1677023 [71] F. HIAI, D. PETZ; Eigenvalue density of the Wishart matrix and large deviations, Inf. Dim. Anal. Quantum Probab. Rel. Top. 1: 633–646 (1998) MR1665279 [72] A. T. JAMES; Distribution of matrix variates and latent roots derived from normal samples, Ann. Math. Stat. 35: 475–501 (1964) MR181057 [73] K. JOHANNSON, The longest increasing subsequence in a random permutation and a unitary random matrix model Math. Res. Lett. 5: 63–82 (1998) MR1618351 [74] K. JOHANSSON; On fluctuations of eigenvalues of random Hermitian matrices, Duke J. Math. 91: 151–204 (1998) MR1487983 [75] K. JOHANSSON; Shape fluctuations and random matrices, Comm. Math. Phys. 209: 437–476 (2000) MR1737991 [76] K. JOHANSSON; Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices, Comm. Math. Phys. 215: 683–705 (2001) MR1810949 [77] K. JOHANSSON; Discrete othogonal polynomial ensembles and the Plancherel measure Ann. Math. 153: 259–296 (2001) MR1826414 [78] K. JOHANSSON; Non-intersecting paths, random tilings and random matrices Probab. Th. Rel. Fields 123 : 225–280 (2002) MR1900323 [79] K. JOHANSSON; Discrete Polynuclear Growth and Determinantal processes Comm. Math. Phys. 242: 277–329 (2003) MR2018275 [80] I.M. JOHNSTONE; On the distribution of the largest principal component, Technical report No 2000-27 [81] D. JONSSON; Some limit theorems for the eigenvalues of a sample covariance matrix, J. Mult. Anal. 12: 151–204 (1982) [82] I. KARATZAS, S. SHREVE, Brownian motion and stocahstic calculus. Second Edition. Graduate Texts in Mathematics 113 Springer-Verlag (1991) MR1121940 [83] KARLIN S.; Coincidence probabilities and applications in combinatorics J. Appl. Prob. 25 A: 185-200 (1988) MR974581 [84] R. KENYON, A. OKOUNKOV, S. SHEFFIELD; Dimers and Amoebae. http://front.math.ucdavis.edu/math-ph/0311005 [85] S. KEROV, Asymptotic representation theory of the symmetric group and its applications in Analysis, AMS (2003) [86] C. KIPNIS and C. LANDIM; Scaling limits of interacting particle systems, Springer (1999) [87] C. KIPNIS and S. OLLA; Large deviations from the hydrodynamical limit for a system of independent Brownian motion Stochastics Stochastics Rep. 33: 17–25 (1990) MR1079929 [88] C. KIPNIS, S. OLLA and S. R. S. VARADHAN; Hydrodynamics and Large Deviation for Simple Exclusion Processes Comm. Pure Appl. Math. 42: 115–137 (1989) MR978701 [89] A. M. KHORUNZHY, B. A. KHORUZHENKO, L. A. PASTUR; Asymptotic properties of large random matrices with independent entries, J. Math. Phys. 37: 5033–5060 (1996) MR1411619 [90] G. MAHOUX, M. MEHTA; A method of integration over matrix variables III, Indian J. Pure Appl. Math. 22: 531–546 (1991) MR1124025 [91] A. MATYTSIN; On the large N-limit of the Itzykson-Zuber integral, Nuclear Physics B411: 805–820 (1994) [92] A. MATYTSIN, P. ZAUGG; Kosterlitz-Thouless phase transitions on discretized random surfaces, Nuclear Physics B497: 699–724 (1997) MR1463643 [93] M. L. MEHTA; Random matrices, 2nd ed. Academic Press (1991) [94] M. L. MEHTA; A method of integration over matrix variables, Comm. Math. Phys. 79: 327–340 (1981) MR627056 [95] I. MINEYEV, D. SHLYAKHTENKO; Non-microstates free entropy dimension for groups http://front.math.ucdavis.edu/math.OA/0312242 [96] J. MINGO , R. SPEICHER; Second order freeness and Fluctuations of Random Matrices : I. Gaussian and Wishart matrices and cyclic Fock spaces http://front.math.ucdavis.edu/math.OA/0405191 [97] J. MINGO; R. SPEICHER; P. SNIADY; Second order freeness and Fluctuations of Random Matrices : II. Unitary random matrices http://front.math.ucdavis.edu/math.OA/0405258 [98] H. MONTGOMERY, Corrélations dans l’ensemble des zéros de la fonction zêta, Publ. Math. Univ. Bordeaux Année I (1972) [99] A. M. ODLYZKO; The 1020 zero of the Riemann zeta function and 70 Million of its neighbors, Math. Comput. 48: 273–308 (1987) [100] A. M. ODLYZKO; The 1022-nd zero of the Riemann zeta function.Amer. Math. Soc., Contemporary Math. Series 290: 139–144 (2002) [101] A. OKOUNKOV; The uses of random partitions http://front.math.ucdavis.edu/math-ph/0309015 [102] L.A. PASTUR, Universality of the local eigenvalue statistics for a class of unitary random matrix ensembles J. Stat. Phys. 86: 109–147 (1997) MR1435193 [103] L.A. PASTUR, V.A MARTCHENKO; The distribution of eigenvalues in certain sets of random matrices, Math. USSR-Sbornik 1: 457–483 (1967) [104] G.K. PEDERSEN, C*-algebras and their automorphism groups, London mathematical society monograph 14 (1989) [105] R.T. ROCKAFELLAR, Convex Analysis Princeton university press (1970) [106] H. ROST; Nonequilibrium behaviour of a many particle process : density profile and local equilibria Z. Wahrsch. Verw. Gebiete 58: 41–53 (1981) MR635270 [107] B. SAGAN; The symmetric group. The Wadsworth Brooks/Cole Mathematics Series (1991) [108] D. SERRE; Sur le principe variationnel des équations de la mécanique des fluides parfaits. Math. Model. Num. Analysis 27: 739–758 (1993) MR1246997 [109] D. SHLYAKHTENKO; Random Gaussian Band matrices and Freeness with Amalgation Int. Math. Res. Not. 20 1013–1025 (1996) MR1422374 [110] Ya. SINAI, A. SOSHNIKOV; A central limit theorem for traces of large random matrices with independent matrix elements, Bol. Soc. Brasil. Mat. (N.S.) 29: 1–24 (1998). MR1620151 [111] P. SNIADY; Multinomial identities arising from free probability theory J. Combin. Theory Ser. A 101: 1–19 (2003) MR1953277 [112] A. SOSHNIKOV; Universality at the edge of the spectrum in Wigner random matrices, Comm. Math. Phys. 207: 697–733 (1999) MR1727234 [113] R. SPEICHER; Free probability theory and non-crossing partitions Sem. Lothar. Combin. 39 (1997) [114] H. SPOHN, M. PRAHOFER; Scale invariance of the PNG droplet and the Airy process J. Statist. Phys. 108: 1071–1106 (2002) MR1933446 [115] V.S. SUNDER, An invitation to von Neumann algebras, Universitext, Springer(1987) [116] I. TELATAR, D. TSE ; Capacity and mutual information of wideband multipath fading channels. IEEE Trans. Inform. Theory 46 no. 4, 1384–1400 (2000) MR1768556 [117] C. TRACY, H. WIDOM; Level spacing distribution and the Airy kernel Comm. Math. Phys. 159: 151–174 (1994) MR1257246 [118] C. A. TRACY, H. WIDOM; Universality of the distribution functions of random matrix theory, Integrable systems : from classical to quantum, CRM Proc. Lect. Notes 26: 251–264 (2001) MR1791893 [119] F. G. TRICOMI; Integral equations, Interscience, New York (1957) [120] D. TSE, O. ZEITOUNI; Linear multiuser receivers in random environments, IEEE trans. IT. 46: 171–188 (2000) [121] D. VOICULESCU; Limit laws for random matrices and free products Invent. math. 104: 201–220 (1991) MR1094052 [122] D. VOICULESCU; The analogues of Entropy and Fisher’s Information Measure in Free Probability Theory jour Commun. Math. Phys. 155: 71–92 (1993) MR1228526 [123] D. VOICULESCU; The analogues of Entropy and Fisher’s Information Measure in Free Probability Theory, IIInvent. Math. 118: 411–440 (1994) MR1296352 [124] D.V. VOICULESCU,The analogues of Entropy and Fisher’s Information Measure in Free Probability Theory, III. The absence of Cartan subalgebras Geom. Funct. Anal. 6: 172–199 (1996) MR1371236 [125] D. VOICULESCU; The analogues of Entropy and Fisher’s Information Measure in Free Probability Theory, V : Noncommutative Hilbert Transforms Invent. Math. 132: 189–227 (1998) MR1618636 [126] D. VOICULESCU; A Note on Cyclic Gradients Indiana Univ. Math. I 49: 837–841 (2000) MR1803213 [127] D.V. VOICULESCU, A strengthened asymptotic freeness result for random matrices with applications to free entropy.Interat. Math. Res. Notices 1: 41–63 ( 1998) MR1601878 [128] D. VOICULESCU; Lectures on free probability theory, Lecture Notes in Mathematics 1738: 283–349 (2000). [129] D. VOICULESCU;Free entropy Bull. London Math. Soc. 34: 257–278 (2002) MR1887698 [130] H. WEYL; The Classical Groups. Their Invariants and Representations Princeton University Press (1939) MR255 [131] E. WIGNER; On the distribution of the roots of certain symmetric matrices, Ann. Math. 67: 325–327 (1958). MR95527 [132] J. WISHART; The generalized product moment distribution in samples from a normal multivariate population, Biometrika 20: 35–52 (1928). MR937 [133] S. ZELDITCH; Macdonald’s identities and the large N limit of Y M2 on the cylinder, Comm. Math. Phys. 245, 611–626 (2004) MR2045685 [134] P. ZINN-JUSTIN; Universality of correlation functions of hermitian random matrices in an external field, Comm. Math. Phys. 194: 631–650 (1998). MR1631489 [135] P. ZINN-JUSTIN; The dilute Potts model on random surfaces, J. Stat. Phys. 98: 245–264 (2000) [136] A. ZVONKIN, Matrix integrals and Map enumeration; an accessible introduction Math. Comput. Modelling 26 : 281–304 (1997) MR1492512 |
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