The semicircle law, free random variables and entropy:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2000
|
| Series: | Mathematical surveys and monographs
77 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 376 Seiten |
| ISBN: | 9780821841358 0821820818 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents Preface ix Overview 1 The isomorphism problem of free group factors.................................. 1 0.2 From the relationof free generators to free probability........................ 3 0.3 Random matrices....................................................................................... 5 0.4 Entropy and large deviations.................................................................. 9 0.1 0.5 Voiculescu’s freeentropy formultivariables 0.6 Operator algebras ......................................... 12 ............................................................................. 14 1 Probability LawsandNoncommutativeRandom Variables 19 1.1 Distribution measure of normal operators............................................ 20 1.2 Noncommutative random variables........................................................ 32 2 The Free Relation 39 2.1 The free product of noncommutative probability spaces ................... 40 2.2 The free relation....................................................................................... 42 2.3 The 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, andHilbert
transform................. 92 3.2 Relation between Cauchy transform andR-series................................ 95 3.3 Infinitely divisible laws.............................................................................. 98 vii
CONTENTS viii 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 The 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 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 Bibliography 357 Index 371
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:43:06Z |
| institution | BVB |
| isbn | 9780821841358 0821820818 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009056873 |
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| physical | X, 376 Seiten |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Hiai, Fumio 1948- Verfasser (DE-588)124955878 aut The semicircle law, free random variables and entropy Fumio Hiai ; Dénes Petz Providence, RI American Math. Soc. 2000 X, 376 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 77 Stochastische Matrix (DE-588)4057624-3 gnd rswk-swf Entropie (DE-588)4014894-4 gnd rswk-swf Stochastische Matrix (DE-588)4057624-3 s Entropie (DE-588)4014894-4 s DE-604 Petz, Dénes 1953- Verfasser (DE-588)174104006 aut Erscheint auch als Online-Ausgabe 978-1-4704-1304-0 Mathematical surveys and monographs 77 (DE-604)BV000018014 77 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009056873&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hiai, Fumio 1948- Petz, Dénes 1953- The semicircle law, free random variables and entropy Mathematical surveys and monographs Stochastische Matrix (DE-588)4057624-3 gnd Entropie (DE-588)4014894-4 gnd |
| subject_GND | (DE-588)4057624-3 (DE-588)4014894-4 |
| title | The semicircle law, free random variables and entropy |
| title_auth | The semicircle law, free random variables and entropy |
| title_exact_search | The semicircle law, free random variables and entropy |
| title_full | The semicircle law, free random variables and entropy Fumio Hiai ; Dénes Petz |
| title_fullStr | The semicircle law, free random variables and entropy Fumio Hiai ; Dénes Petz |
| title_full_unstemmed | The semicircle law, free random variables and entropy Fumio Hiai ; Dénes Petz |
| title_short | The semicircle law, free random variables and entropy |
| title_sort | the semicircle law free random variables and entropy |
| topic | Stochastische Matrix (DE-588)4057624-3 gnd Entropie (DE-588)4014894-4 gnd |
| topic_facet | Stochastische Matrix Entropie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009056873&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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