Free random variables: a noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, R.I.
American Math. Soc.
1992
|
| Schriftenreihe: | Centre de Recherches Mathématiques <Montréal>: CRM Monograph series
1 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005240078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | V, 70 S. |
| ISBN: | 082186999X |
Internformat
MARC
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| 245 | 1 | 0 | |a Free random variables |b a noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups |c D. V. Voiculescu ; K. J. Dykema ; A. Nica |
| 264 | 1 | |a Providence, R.I. |b American Math. Soc. |c 1992 | |
| 300 | |a V, 70 S. | ||
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| 700 | 1 | |a Nica, Andu |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1819299885406486528 |
|---|---|
| adam_text | Contents
Preface v
Chapter 1. Free Products 1
1.1. Groups 1
1.2. Unital algebras 1
1.3. Hilbert spaces 3
1.4. Unital C algebras 3
1.5. Representations and states 4
1.6. The commutant of a free product 7
Chapter 2. Free Random Variables in Noncommutative
Probability Theory 11
2.1. Introduction 11
2.2. Noncommutative probability spaces 12
2.3. Random variables in noncommutative probability spaces 12
2.4. Independence 13
2.5. Freeness 14
2.6. Analogue of the Gaussian process over a Hilbert space 17
Chapter 3. Free Harmonic Analysis 21
3.1. Additive free convolution 21
3.2. The R transform 22
3.3. Analytic function theory for the R transform 23
3.4. Examples 26
3.5. The central limit theorem 28
3.6. Multiplicative free convolution 29
3.7. Infinite divisibility 32
3.8. Free products with amalgamation 37
Chapter 4. Random Matrices and Asymptotic Freeness 43
4.1. Complex Gaussian random matrices 44
4.2. Further results 50
4.3. Random unitary matrices 52
4.4. The non Gaussian case 54
iii
iv CONTENTS
Chapter 5. Free Product Factors 55
5.1. Circular and semicircular systems 55
5.2. Direct applications 59
5.3. The fundamental group of L(Foo) 62
5.4. Free products with injective factors 63
Postscript 67
References 69
|
| any_adam_object | 1 |
| author | Voiculescu, Dan 1949- Dykema, Ken J. Nica, Andu |
| author_GND | (DE-588)122093968 |
| author_facet | Voiculescu, Dan 1949- Dykema, Ken J. Nica, Andu |
| author_role | aut aut aut |
| author_sort | Voiculescu, Dan 1949- |
| author_variant | d v dv k j d kj kjd a n an |
| building | Verbundindex |
| bvnumber | BV007928394 |
| classification_rvk | SK 600 UB 4056 |
| ctrlnum | (OCoLC)260194746 (DE-599)BVBBV007928394 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV007928394 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:14:20Z |
| institution | BVB |
| isbn | 082186999X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005240078 |
| oclc_num | 260194746 |
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| physical | V, 70 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Centre de Recherches Mathématiques <Montréal>: CRM Monograph series |
| series2 | Centre de Recherches Mathématiques <Montréal>: CRM Monograph series |
| spellingShingle | Voiculescu, Dan 1949- Dykema, Ken J. Nica, Andu Free random variables a noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups Centre de Recherches Mathématiques <Montréal>: CRM Monograph series Selbstadjungierter Operator (DE-588)4180810-1 gnd Freie Gruppe (DE-588)4155283-0 gnd Operatoralgebra (DE-588)4129366-6 gnd |
| subject_GND | (DE-588)4180810-1 (DE-588)4155283-0 (DE-588)4129366-6 |
| title | Free random variables a noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups |
| title_auth | Free random variables a noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups |
| title_exact_search | Free random variables a noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups |
| title_full | Free random variables a noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups D. V. Voiculescu ; K. J. Dykema ; A. Nica |
| title_fullStr | Free random variables a noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups D. V. Voiculescu ; K. J. Dykema ; A. Nica |
| title_full_unstemmed | Free random variables a noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups D. V. Voiculescu ; K. J. Dykema ; A. Nica |
| title_short | Free random variables |
| title_sort | free random variables a noncommutative probability approach to free products with applications to random matrices operator algebras and harmonic analysis on free groups |
| title_sub | a noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups |
| topic | Selbstadjungierter Operator (DE-588)4180810-1 gnd Freie Gruppe (DE-588)4155283-0 gnd Operatoralgebra (DE-588)4129366-6 gnd |
| topic_facet | Selbstadjungierter Operator Freie Gruppe Operatoralgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005240078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007928388 |
| work_keys_str_mv | AT voiculescudan freerandomvariablesanoncommutativeprobabilityapproachtofreeproductswithapplicationstorandommatricesoperatoralgebrasandharmonicanalysisonfreegroups AT dykemakenj freerandomvariablesanoncommutativeprobabilityapproachtofreeproductswithapplicationstorandommatricesoperatoralgebrasandharmonicanalysisonfreegroups AT nicaandu freerandomvariablesanoncommutativeprobabilityapproachtofreeproductswithapplicationstorandommatricesoperatoralgebrasandharmonicanalysisonfreegroups |