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- catalog contributor b11616179.
- catalog contributor b11616180.
- catalog created "c2000.".
- catalog date "2000".
- catalog date "c2000.".
- catalog dateCopyrighted "c2000.".
- catalog description "0.1 Isomorphism problem of free group factors 1 -- 0.2 From the relation of free generators to free probability 3 -- 0.3 Random matrices 5 -- 0.4 Entropy and large deviations 9 -- 0.5 Voiculescu's free entropy for multivariables 12 -- 0.6 Operator algebras 14 -- 1 Probability Laws and Noncommutative Random Variables 19 -- 1.1 Distribution measure of normal operators 20 -- 1.2 Noncommutative random variables 32 -- 2 Free Relation 39 -- 2.1 Free product of noncommutative probability spaces 40 -- 2.2 Free relation 42 -- 2.3 Free central limit theorem 48 -- 2.4 Free convolution of measures 52 -- 2.5 Moments and cumulants 60 -- 2.6 Multivariables 71 -- 3 Analytic Function Theory and Infinitely Divisible Laws 91 -- 3.1 Cauchy transform, Poisson integral, and Hilbert transform 92 -- 3.2 Relation between Cauchy transform and R-series 95 -- 3.3 Infinitely divisible laws 98 --".
- catalog description "4 Random Matrices and Asymptotically Free Relation 113 -- 4.1 Random matrices and their eigenvalues 114 -- 4.2 Random unitary matrices and asymptotic freeness 135 -- 4.3 Asymptotic freeness of some random matrices 146 -- 4.4 Random matrix models of noncommutative random variables 161 -- 5 Large Deviations for Random Matrices 175 -- 5.1 Boltzmann entropy and large deviations 176 -- 5.2 Entropy and random matrices 181 -- 5.3 Logarithmic energy and free entropy 189 -- 5.4 Gaussian and unitary random matrices 209 -- 5.5 Wishart matrix 226 -- 5.6 Entropy and large deviations revisited 239 -- 6 Free Entropy of Noncommutative Random Variables 245 -- 6.1 Definition and basic properties 246 -- 6.2 Calculus for power series of noncommutative variables 253 -- 6.3 Change of variable formulas for free entropy 259 -- 6.4 Additivity of free entropy 269 -- 6.5".
- catalog description "Free entropies of unitary and non-selfadjoint random variables 275 -- 6.6 Relation between different free entropies 280 -- 7 Relation to Operator Algebras 301 -- 7.1 Free group factors and semicircular systems 302 -- 7.2 Interpolated free group factors 310 -- 7.3 Free entropy dimension 327 -- 7.4 Applications of free entropy 346.".
- catalog description "Includes bibliographical references (p. 357-369) and index.".
- catalog extent "x, 376 p. ;".
- catalog identifier "0821820818 (alk. paper)".
- catalog isPartOf "Mathematical surveys and monographs ; no. 77.".
- catalog isPartOf "Mathematical surveys and monographs, 0076-5376 ; v. 77".
- catalog issued "2000".
- catalog issued "c2000.".
- catalog language "eng".
- catalog publisher "Providence, RI : American Mathematical Society,".
- catalog subject "512/.55 21".
- catalog subject "Entropy.".
- catalog subject "Free probability theory.".
- catalog subject "QA326 .H52 2000".
- catalog subject "Random matrices.".
- catalog tableOfContents "0.1 Isomorphism problem of free group factors 1 -- 0.2 From the relation of free generators to free probability 3 -- 0.3 Random matrices 5 -- 0.4 Entropy and large deviations 9 -- 0.5 Voiculescu's free entropy for multivariables 12 -- 0.6 Operator algebras 14 -- 1 Probability Laws and Noncommutative Random Variables 19 -- 1.1 Distribution measure of normal operators 20 -- 1.2 Noncommutative random variables 32 -- 2 Free Relation 39 -- 2.1 Free product of noncommutative probability spaces 40 -- 2.2 Free relation 42 -- 2.3 Free central limit theorem 48 -- 2.4 Free convolution of measures 52 -- 2.5 Moments and cumulants 60 -- 2.6 Multivariables 71 -- 3 Analytic Function Theory and Infinitely Divisible Laws 91 -- 3.1 Cauchy transform, Poisson integral, and Hilbert transform 92 -- 3.2 Relation between Cauchy transform and R-series 95 -- 3.3 Infinitely divisible laws 98 --".
- catalog tableOfContents "4 Random Matrices and Asymptotically Free Relation 113 -- 4.1 Random matrices and their eigenvalues 114 -- 4.2 Random unitary matrices and asymptotic freeness 135 -- 4.3 Asymptotic freeness of some random matrices 146 -- 4.4 Random matrix models of noncommutative random variables 161 -- 5 Large Deviations for Random Matrices 175 -- 5.1 Boltzmann entropy and large deviations 176 -- 5.2 Entropy and random matrices 181 -- 5.3 Logarithmic energy and free entropy 189 -- 5.4 Gaussian and unitary random matrices 209 -- 5.5 Wishart matrix 226 -- 5.6 Entropy and large deviations revisited 239 -- 6 Free Entropy of Noncommutative Random Variables 245 -- 6.1 Definition and basic properties 246 -- 6.2 Calculus for power series of noncommutative variables 253 -- 6.3 Change of variable formulas for free entropy 259 -- 6.4 Additivity of free entropy 269 -- 6.5".
- catalog tableOfContents "Free entropies of unitary and non-selfadjoint random variables 275 -- 6.6 Relation between different free entropies 280 -- 7 Relation to Operator Algebras 301 -- 7.1 Free group factors and semicircular systems 302 -- 7.2 Interpolated free group factors 310 -- 7.3 Free entropy dimension 327 -- 7.4 Applications of free entropy 346.".
- catalog title "The semicircle law, free random variables, and entropy / Fumio Hiai, Dénes Petz.".
- catalog type "text".