random matrices 142 pure and applied mathematics

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Random Matrices

Author : Madan Lal Mehta
ISBN : 008047411X
Genre : Mathematics
File Size : 82. 17 MB
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Random Matrices gives a coherent and detailed description of analytical methods devised to study random matrices. These methods are critical to the understanding of various fields in in mathematics and mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, chaotic systems, the zeros of the Riemann and other zeta functions. More generally they apply to the characteristic energies of any sufficiently complicated system and which have found, since the publication of the second edition, many new applications in active research areas such as quantum gravity, traffic and communications networks or stock movement in the financial markets. This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time. Presentation of many new results in one place for the first time. First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals. Fredholm determinants and Painlevé equations. The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities. Fredholm determinants and inverse scattering theory. Probability densities of random determinants.

Large Random Matrices

Author : Alice Guionnet
ISBN : 9783540698968
Genre : Mathematics
File Size : 73. 86 MB
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These lectures emphasize the relation between the problem of enumerating complicated graphs and the related large deviations questions. Such questions are closely related with the asymptotic distribution of matrices.

Random Matrix Theory

Author : Percy Deift
ISBN : 9780821883570
Genre : Mathematics
File Size : 42. 76 MB
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"This book features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles-orthogonal, unitary, and symplectic. The authors follow the approach of Tracy and Widom, but the exposition here contains a substantial amount of additional material, in particular, facts from functional analysis and the theory of Pfaffians. The main result in the book is a proof of universality for orthogonal and symplectic ensembles corresponding to generalized Gaussian type weights following the authors' prior work. New, quantitative error estimates are derived." --Book Jacket.

Patterned Random Matrices

Author : Arup Bose
ISBN : 9780429948893
Genre : Mathematics
File Size : 42. 29 MB
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Large dimensional random matrices (LDRM) with specific patterns arise in econometrics, computer science, mathematics, physics, and statistics. This book provides an easy initiation to LDRM. Through a unified approach, we investigate the existence and properties of the limiting spectral distribution (LSD) of different patterned random matrices as the dimension grows. The main ingredients are the method of moments and normal approximation with rudimentary combinatorics for support. Some elementary results from matrix theory are also used. By stretching the moment arguments, we also have a brush with the intriguing but difficult concepts of joint convergence of sequences of random matrices and its ramifications. This book covers the Wigner matrix, the sample covariance matrix, the Toeplitz matrix, the Hankel matrix, the sample autocovariance matrix and the k-Circulant matrices. Quick and simple proofs of their LSDs are provided and it is shown how the semi-circle law and the March enko-Pastur law arise as the LSDs of the first two matrices. Extending the basic approach, we also establish interesting limits for some triangular matrices, band matrices, balanced matrices, and the sample autocovariance matrix. We also study the joint convergence of several patterned matrices, and show that independent Wigner matrices converge jointly and are asymptotically free of other patterned matrices. Arup Bose is a Professor at the Indian Statistical Institute, Kolkata, India. He is a distinguished researcher in Mathematical Statistics and has been working in high-dimensional random matrices for the last fifteen years. He has been the Editor of Sankyhā for several years and has been on the editorial board of several other journals. He is a Fellow of the Institute of Mathematical Statistics, USA and all three national science academies of India, as well as the recipient of the S.S. Bhatnagar Award and the C.R. Rao Award. His forthcoming books are the monograph, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee), to be published by Chapman & Hall/CRC Press, and a graduate text, U-statistics, M-estimates and Resampling (with Snigdhansu Chatterjee), to be published by Hindustan Book Agency.

Random Matrix Theory Interacting Particle Systems And Integrable Systems

Author : Percy Deift
ISBN : 9781107079922
Genre : Language Arts & Disciplines
File Size : 43. 53 MB
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This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles.

Bulletin New Series Of The American Mathematical Society

Author :
ISBN : UOM:39015072629788
Genre : Mathematics
File Size : 80. 6 MB
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Probabilistic Methods In Applied Mathematics

Author : Albert T. Bharucha-Reid
ISBN : MINN:319510000443514
Genre : Mathematics
File Size : 33. 22 MB
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ISBN : OSU:32435021938972
Genre : Science
File Size : 56. 34 MB
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Subject Guide To Books In Print

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ISBN : STANFORD:36105025888533
Genre : American literature
File Size : 29. 58 MB
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Encyclopedia Of Mathematical Physics

Author : Jean-Pierre Françoise
ISBN : 0125126603
Genre :
File Size : 65. 78 MB
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