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Mehta M.L. — Random Matrices
Mehta M.L. — Random Matrices

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Название: Random Matrices

Автор: Mehta M.L.

Аннотация:

Since the publication of Random Matrices (Academic Press, 1967) so many new results have emerged both in theory and in applications, that this edition is almost completely revised to reflect the developments. For example, the theory of matrices with quaternion elements was developed to compute certain multiple integrals, and the inverse scattering theory was used to derive asymptotic results. The discovery of Selberg's 1944 paper on a multiple integral also gave rise to hundreds of recent publications.
This book presents a coherent and detailed analytical treatment of random matrices, leading in particular to the calculation of n-point correlations, of spacing probabilities, and of a number of statistical quantities. The results are used in describing the statistical properties of nuclear excitations, the energies of chaotic systems, the ultrasonic frequencies of structural materials, the zeros of the Riemann zeta function, and in general the characteristic energies of any sufficiently complicated system. Of special interest to physicists and mathematicians, the book is self-contained and the reader need know mathematics only at the undergraduate level.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3rd edition

Год издания: 2004

Количество страниц: 688

Добавлена в каталог: 01.07.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Lambda$-statistic      303
Abramowitz, M.      228 641
Airy function      452
Airy kernel      452 54 531
Andrews, G.E.      309 311 649
Angular momentum operator      36
Anti-symmetric      36 41 74 499
Anti-symmetric Hermitian matrices      48 59 237
Antiunitary operator      34
Aomoto's extension      310
Aomoto, K.      651
Artin, E.      283
Askey, R.A.      309 311 324 651
Asymptotic expansion      139 350 352 396
Asymptotic formula      65 67 337
Asymptotic series      336
Asymptotics of $\lambda_{n}(t)$      336
Asymptotics of Toeplitz determinants      339
Averages with Laguerre or Hermite weights      323
Baik, J.      468
Balazs, N.L.      32
Balian, R.      7 62 649
Bateman, H.      141 142 228 285 354 355 362 420 475 476 511 512 556 572 640 641
Berry, M.V.      291
Bessel function      461
Bethe, H.A.      8 649
Bi-orthogonal polynomials      72 88 102 103 109 441 447 650
Bi-orthogonal polynomials, zeros of      106 443 448
Binary quadratic forms      27 642
Bohigas, O.      11 16 172 173 292 293 296 297 304 649
Bohr, A.      9
Brezin, E.      410
Brody, T.A.      10 16 307 649
Bronk, B.V.      449 451 492 652
Brownian motion      5 184 650
Brownian Motion Model      185 203 221 509
Bureau, F.J.      406
Caillol, J.M.      330
Camarda, H.S.      2 289
Cameron, A.G.W.      8 649
Carlson's theorem      226 314
Cauchy transform      423
Cayley — Klein parameters      330
Chadan, K.      341
Chandrasekhar, S.      183
Change of variables      636
Chaotic systems      1
Characteristic function      507
Characteristic polynomial      79
Chevalley, C.      38
Christoffel — Darboux formula      511
Chu, L.J.      137 138
Cicuta, G.M.      651
Cipra, B.A.      20 649
Circular ensembles      4 47 323
Circular orthogonal ensemble      646
Circular symplectic ensemble      646
Circular unitary ensemble      20 30 461 646
Class function      26 643
Cluster function      111 144 148 177 203 207 216 263 514 650
Cluster function, n-level      152
Cluster function, two-level      110 120 152 178
COE      646
Complex conjugate      39
Complex matrices      266 573
Computer proof      326
Confluences      627
Confluent alternant      104
Conjecture      7 494 653
conjugate      74
Conjugate quaternion      39
Conte, R.      622 623 654
Continuum model      231
Contour map      134 136
Convolution      634
Convolution integrals      558
Corbato, F.J.      137 138
Correlation      34 111 148 177
Correlation function      4 15 79 81 87 89 111 203 207 216 237 263 428 435 436 448
Correlation function, n-point      118
Correlation function, two-level      121
Cosgrove, C.M.      404
Coulomb gas model      182
Coupled matrices      426
Covariance of the consecutive spacings      301
Coxeter indices      325 648
Coxeter symbol      326
CSE      646
Cue      646 647 649
Davenport, H.      26 649
de Bruijn, N.G.      96 414
Deift, P.      xiii 108 468
Delande, D.      32
Delannay, R.      6 485 490 652 653
Des Cloizeaux, J.      337 339 650 652 653
Desjardins, J.S.      2 4
Determinant      72 412 415 538 539 541 542 545 547 549
Determinants: probability densities      281 469
di Francesco, R.      xiii 32 649
Diagonalization      577
Dietz, B.      520 652
Dieudonne, J.      38
Differential equations      384 394
Dirichlet series      29
Discriminant      26
Dual      40 75
Dyson, F.J.      4—6 47 64 73—75 111 183 191 295 300 385 406 408 525 649—652
Eckhardt, B.      649
Edelman, A.      266 279 281 588 594 651 654
Effetof, K.B.      xiii 650
Eigenfunctions      33 125
Eigenvalues      4—6 125 126
Eliashberg, G.M.      15
Energy      228
energy levels      2 3 5 7 8
Energy statistic      298
Ensemble averages      187
Ensembles from GOE to GUE and beyond      245 256
Ensembles from GSE to GUE and beyond      250 260
entropy      64 65 228 232
Epstein zeta function      27
Ercolani, N.M.      107 441 650
Erdelyi, A.      511
Erdos, P.      460
Ergodic theorem      140
Ergodicity      140
Error function      484
Exceptional groups      326
Excess      303—305
Extensive quantity      232
Eynard, B.      103 650 652
F-statistic      302
Feshbach, H.      502
Finite reflection groups      325
Fission widths      9
Fixed strength ensemble      47 487
Flores, J.      10 16 307 649
Fokas, A.S.      108
Fokker — Planck equation      184
Form-factor      146
Form-factor, n -level      122 154 179
Form-factor, two-level      121 179
Forrester, P.J.      421
Fourier transform      110 144 154 514 526
Fox, D.      47
Fredholm determinant      133 134 335 336 340—342 352 382 436 448 452 454 457
Fredholm theory of integral equations      110
Free energy      65
French, J.B.      10 16 307 509 649
Frohlich, H.      5 15
Fyodorov, Y.V.      423 424 652
Garg, J.B.      2
Garvan, F.G.      326
Gaudin, M.      65
Gaussian      133
Gaussian ensemble      4 12 33 50 63 498 646
Gaussian ensemble of Hermitian anti-symmetric matrices      62
Gaussian ensemble with unequal real and imaginary parts      60
Gaussian orthogonal ensemble      7 12—14 36 58 146 480 482 483 607 608 645
Gaussian symplectic ensemble      7 38 58 477 646
Gaussian unitary ensemble      7 20 24 42 58 134 146 452 473 609 610 645
Gay, J.C.      32
Gel'fand — Levitan method      341 342
Gel'fand, I.M.      341
Generalization of the beta integral      327
Generating function      140 437 448 506
Gessel, I.M.      461
Ghosh, S.      103 360 362 363 650 652
Giannoni, M.J.      11 172 173 293 296
Ginibre, J.      266 267 281 573 651
Ginsparg, P.      xiii 32 649
Girko, V.L.      xiii
Global property      6 7
GOE      146 645 647
Good, I.J.      226
Gorkov, L.P.      15
Goursat, E.      134 385 454
Gradshteyn, I.S.      235 640
Gram's formula      516
Gromak, V.I.      404 406
GSE      646
GUE      468 645 647
Guhr, t.      xiii 32 649
Haake, F.      520
Hacken, G.      2 289
Hamiltonian      3 33
Hamiltonian equations      624 654
Hammersley, J.M.      460
Haq, R.U.      16 292 297 304 649
Hardy — Ramanujan formula      8 649
Harer, J.      140
Harish-Chandra      648
Harvey, J.A.      4
Hastings, S.P.      532
Havens Jr., W.W.      2 4
Heilbronn, H.      26 649
Hermite polynomials      47 118 149 176 556
Hermitian      8
Hermitian matrices coupled in a linear chain      647
Hikami, S.      410
Hua, L.K.      285
Hughes, D.J.      4
Hurwitz zeta functions      29
Incomplete gamma function      269
Inflection point      450
information      61
Information theory      60
Integer moments      285 483
Integral equation      124 126
Integral representation      650
Integration over alternate variables      84—87 154 159 160 650
Inverse Mellin transform      475 479 482 484
Inverse power series      629
Inverse scattering      336 340
Ising model      6
Its, A.R      108 402
Itzykson, C.      644
Jacobi polynomials      354 355
Jacobian      51 193
James, A.T.      364
Jancovici, B.      651
Jensen, J.H.D.      2
Jimbo, M.      382 385 394 405
Joint probability density      43 58 62 565
Joint probability density of the eigenvalues      197 254
Jost, R.      344
Kahn, P.B.      47 650
Katz, N.M.      xiii 30 32
Keating, J.      23 27 28 649
Kernel      119 124 125 436
Kerov, C.V.      460
Khinchin, A.I.      61
Kisslinger, L.S.      2
Kitaev, A.V.      108
Kostlan, E.      266 279 588 651 654
Kota, V.K.B.      16 509 649
Kramer's degeneracy      54
Kramer, H.A.      54
Kubo, R.      15
Kullback, S.      281
Laguerre polynomials      356
Landau, L.      14
Lang, J.M.B.      8 649
Laplace manner      85 127
Lax pairs      621 654
Le Caer, G.      6 485 490 652 653
Least square statistic      294
Lecouteur, K.J.      8 649
Leff, H.S.      47
Legendre polynomials      137 518
Level density      8 10 63 65 67 119 120 237 356 450
Level spacing      10 113 122 154 179 180 205 213 219 240
Levinson, N.      346
Levitan, B.M.      341
Lie algebra      648
Lie group      648 653
Lin, R.      622 623 654
Linear statistic      601
Liou, H.I.      2 289
Lipschitz condition      339
Little, J.D.C.      137 138
Local property      6 7
Logan, B.F.      460
Longest increasing subsequence      460
Luck, J.-M.      644
Lukashevich, N.A.      404 406
Luke, Y.L.      476 640—642
MacDonald, I.G.      44 325 651
Mahoux, G.      650 652
Marchenko method      341 347
Marchenko, V.A.      342
Matrices: Hermitian, unitary, symmetric, self-dual      498
Mayer, M.G.      2
McCoy, B.M.      6 352 405
McLaughlin, K.T.-R.      107 441 650
McLeod, J.B.      532
Mehta, M.L.      44 65 72 73 75 76 80 82 87 94 100 104 127—129 158 216 246 264 282 295 300 325 337 339 364 413 415 416 439 444 476 477 498 504 516 536 561 565 576 582 590 650 653
Meijer G-function      284 476 479 482 491 640
Mellin transform      284 470—473 491
Mello, P.A.      10 16 307 649
Metallic particles      5 15
Mezzadri, F.      24
Miwa, T.      382 385 394 405
Mixed sequence      495
Moment matrix      448
Moments      471
Moments of the characteristic polynomial      409
Monahan, J.E.      303
Montgomery's conjecture      21
Montgomery, H.L.      5 19 649
Moore, C.E.      4
Moore, E.H.      73
Mori, Y.      382 385 394 405
Morris, W.G.      320 651
Morse, P.M.      137 138 502
Moussa, P.      644
Mtiler-Groeling, A.      xiii 32 649
Musette, M.      622 623 654
Mushkelishvili, N.I.      66
N -level correlation function      146 271
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