Lectures on the combinatorics of free probability:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambrigde Univ. Press
2006
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society lecture notes series
335 |
| Subjects: | |
| Online Access: | Beschreibung für Leser Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XV, 417 S. graph. Darst. |
| ISBN: | 9780521858526 0521858526 |
Staff View
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Record in the Search Index
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| adam_text | LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES: 335 LECTURES ON THE
COMBINATORICS OF FREE PROBABILITY ALEXANDRA NICA UNIVERSITY OF WATERLOO,
ONTARIO ROLAND SPEICHER QUEEN S UNIVERSITY, ONTARIO SUB GSTTINGEN 7 219
195 900 2006 A 21007 CAMBRIDGE UNIVERSITY PRESS CONTENTS INTRODUCTION
XIII PART 1. BASIC CONCEPTS 1 LECTURE 1. NON-COMMUTATIVE PROBABILITY
SPACES AND DISTRIBUTIONS 3 NON-COMMUTATIVE PROBABILITY SPACES 3
*-DISTRIBUTIONS (CASE OF NORMAL ELEMENTS) 7 *-DISTRIBUTIONS (GENERAL
CASE) 13 EXERCISES 15 LECTURE 2. A CASE STUDY OF NON-NORMAL DISTRIBUTION
19 DESCRIPTION OF THE EXAMPLE 19 DYCK PATHS 22 THE DISTRIBUTION OF A +
A* 26 USING THE CAUCHY TRANSFORM 30 EXERCISES 33 LECTURE 3.
C*-PROBABILITY SPACES 35 FUNCTIONAL CALCULUS IN A C*-ALGEBRA 35
C*-PROBABILITY SPACES 39 *-DISTRIBUTION, NORM AND SPECTRUM FOR A NORMAL
ELEMENT 43 EXERCISES 46 LECTURE 4. NON-COMMUTATIVE JOINT DISTRIBUTIONS *
49 JOINT DISTRIBUTIONS * 49 JOINT ^-DISTRIBUTIONS 53 JOINT
*-DISTRIBUTIONS AND ISOMORPHISM 55 EXERCISES 59 LECTURE 5. DEFINITION
AND BASIC PROPERTIES OF FREE INDEPENDENCE 63 THE CLASSICAL SITUATION:
TENSOR INDEPENDENCE * 63 DEFINITION OF FREE INDEPENDENCE 64 THE EXAMPLE
OF A FREE PRODUCT OF GROUPS 66 FREE INDEPENDENCE AND JOINT MOMENTS 69
SOME BASIC PROPERTIES OF FREE INDEPENDENCE 71 ARE THERE OTHER UNIVERSAL
PRODUCT CONSTRUCTIONS? 75 VIII CONTENTS EXERCISES 78 LECTURE 6. FREE
PRODUCT OF *-PROBABILITY SPACES 81 FREE PRODUCT OF UNITAL ALGEBRAS 81
FREE PRODUCT OF NON-COMMUTATIVE PROBABILITY SPACES 84 FREE PRODUCT OF
*-PROBABILITY SPACES 86 EXERCISES 92 LECTURE 7. FREE PRODUCT OF
C*-PROBABILITY SPACES 95 THE GNS REPRESENTATION 95 FREE PRODUCT OF
C*-PROBABILITY SPACES 99 EXAMPLE: SEMICIRCULAR SYSTEMS AND THE FULL FOCK
SPACE 102 EXERCISES 109 PART 2. CUMULANTS 113 LECTURE 8. MOTIVATION:
FREE CENTRAL LIMIT THEOREM 115 CONVERGENCE IN DISTRIBUTION 115 GENERAL
CENTRAL LIMIT THEOREM 117 CLASSICAL CENTRAL LIMIT THEOREM 120 FREE
CENTRAL LIMIT THEOREM 121 THE MULTI-DIMENSIONAL CASE 125 CONCLUSION AND
OUTLOOK 131 EXERCISES 132 LECTURE 9. BASIC COMBINATORICS I: NON-CROSSING
PARTITIONS 135 NON-CROSSING PARTITIONS OF AN ORDERED SET 135 THE LATTICE
STRUCTURE OF NC(N) 144 THE FACTORIZATION OF INTERVALS IN NC 14 8
EXERCISES 153 LECTURE 10. BASIC COMBINATORICS II: MOBIUS INVERSION 155
CONVOLUTION IN THE FRAMEWORK OF A POSET 155 MOBIUS INVERSION IN A
LATTICE 160 THE MOBIUS FUNCTION OF NC 162 MULTIPLICATIVE FUNCTIONS ON NC
164 FUNCTIONAL EQUATION FOR CONVOLUTION WITH /X N 168 EXERCISES , 171
LECTURE 11. FREE CUMULANTS: DEFINITION AND BASIC PROPERTIES 173
MULTIPLICATIVE FUNCTIONALS ON NC 173 DEFINITION OF FREE CUMULANTS 175
PRODUCTS AS ARGUMENTS 178 FREE INDEPENDENCE AND FREE CUMULANTS 182
CONTENTS IX CUMULANTS OF RANDOM VARIABLES 185 EXAMPLE: SEMICIRCULAR AND
CIRCULAR ELEMENTS 187 EVEN ELEMENTS 188 APPENDIX: CLASSICAL CUMULANTS
190 EXERCISES 193 LECTURE 12. SUMS OF FREE RANDOM VARIABLES 195 FREE
CONVOLUTION 195 ANALYTIC CALCULATION OF FREE CONVOLUTION 200 PROOF OF
THE FREE CENTRAL LIMIT THEOREM VIA 7?.-TRANSFORM 202 FREE POISSON
DISTRIBUTION 203 COMPOUND FREE POISSON DISTRIBUTION 206 EXERCISES 208
LECTURE 13. MORE ABOUT LIMIT THEOREMS AND INFINITELY DIVISIBLE
DISTRIBUTIONS 211 LIMIT THEOREM FOR TRIANGULAR ARRAYS 211 CUMULANTS OF
OPERATORS ON FOCK SPACE 214 INFINITELY DIVISIBLE DISTRIBUTIONS 215
CONDITIONALLY POSITIVE DEFINITE SEQUENCES 216 CHARACTERIZATION OF
INFINITELY DIVISIBLE DISTRIBUTIONS 220 EXERCISES 221 LECTURE 14.
PRODUCTS OF FREE RANDOM VARIABLES 223 MULTIPLICATIVE FREE CONVOLUTION
223 COMBINATORIAL DESCRIPTION OF FREE MULTIPLICATION 225 COMPRESSION BY
A FREE PROJECTION 228 CONVOLUTION SEMIGROUPS (N M )T I 231 COMPRESSION
BY A FREE FAMILY OF MATRIX UNITS 233 EXERCISES 236 LECTURE 15.
I?-DIAGONAL ELEMENTS % 237 MOTIVATION: CUMULANTS OF HAAR UNITARY
ELEMENTS 237 DEFINITION OF I?-DIAGONAL ELEMENTS 240 SPECIAL
REALIZATIONS OF TRACIAL I?-DIAGONAL ELEMENTS 245 PRODUCT OF TWO FREE
EVEN ELEMENTS 249 THE FREE ANTI-COMMUTATOR OF EVEN ELEMENTS 251 POWERS
OF I?-DIAGONAL ELEMENTS * 253 EXERCISES 254 PART 3. TRANSFORMS AND
MODELS 257 LECTURE 16. THE ^-TRANSFORM 259 THE MULTI-VARIABLE
I?-TRANSFORM 259 X CONTENTS THE FUNCTIONAL EQUATION FOR THE -R-TRANSFORM
265 MORE ABOUT THE ONE-DIMENSIONAL CASE 269 EXERCISES 272 LECTURE 17.
THE OPERATION OF BOXED CONVOLUTION 273 THE DEFINITION OF BOXED
CONVOLUTION, AND ITS MOTIVATION 273 BASIC PROPERTIES OF BOXED
CONVOLUTION 275 RADIAL SERIES 277 THE MOBIUS SERIES AND ITS USE 280
EXERCISES 285 LECTURE 18. MORE ON THE ONE-DIMENSIONAL BOXED CONVOLUTION
287 RELATION TO MULTIPLICATIVE FUNCTIONS ON NC 287 THE 5-TRANSFORM 293
EXERCISES 300 LECTURE 19. THE FREE COMMUTATOR 303 FREE COMMUTATORS OF
EVEN ELEMENTS 303 FREE COMMUTATORS IN THE GENERAL CASE 310 THE
CANCELATION PHENOMENON 314 EXERCISES - 317 LECTURE 20. I?-CYCLIC
MATRICES 321 DEFINITION AND EXAMPLES OF /^-CYCLIC MATRICES 321 THE
CONVOLUTION FORMULA FOR AN /^-CYCLIC MATRIX 324 I?-CYCLIC FAMILIES OF
MATRICES 329 APPLICATIONS OF THE CONVOLUTION FORMULA 331 EXERCISES 335
LECTURE 21. THE FULL FOCK SPACE MODEL FOR THE I?-TRANSFORM 339
DESCRIPTION OF THE FOCK SPACE MODEL 339 AN APPLICATION: REVISITING FREE
COMPRESSIONS 346 EXERCISES 356 LECTURE 22. GAUSSIAN RANDOM MATRICES 359
MOMENTS OF GAUSSIAN RANDOM VARIABLES 359 RANDOM MATRICES IN GENERAL 361
SELFADJOINT GAUSSIAN RANDOM MATRICES AND GENUS EXPANSION 363 ASYMPTOTIC
FREE INDEPENDENCE FOR SEVERAL INDEPENDENT GAUSSIAN RANDOM MATRICES 368
ASYMPTOTIC FREE INDEPENDENCE BETWEEN GAUSSIAN RANDOM MATRICES AND
CONSTANT MATRICES 371 LECTURE 23. UNITARY RANDOM MATRICES 379 HAAR
UNITARY RANDOM MATRICES 379 CONTENTS XI THE LENGTH FUNCTION ON
PERMUTATIONS 381 ASYMPTOTIC FREENESS FOR HAAR UNITARY RANDOM MATRICES
384 ASYMPTOTIC FREENESS BETWEEN RANDOMLY ROTATED CONSTANT MATRICES 385
EMBEDDING OF NON-CROSSING PARTITIONS INTO PERMUTATIONS 390 EXERCISES
,393 NOTES AND COMMENTS 395 REFERENCES 405 INDEX 411
|
| adam_txt |
LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES: 335 LECTURES ON THE
COMBINATORICS OF FREE PROBABILITY ALEXANDRA NICA UNIVERSITY OF WATERLOO,
ONTARIO ROLAND SPEICHER QUEEN'S UNIVERSITY, ONTARIO SUB GSTTINGEN 7 219
195 900 2006 A 21007 CAMBRIDGE UNIVERSITY PRESS CONTENTS INTRODUCTION
XIII PART 1. BASIC CONCEPTS 1 LECTURE 1. NON-COMMUTATIVE PROBABILITY
SPACES AND DISTRIBUTIONS 3 NON-COMMUTATIVE PROBABILITY SPACES 3
*-DISTRIBUTIONS (CASE OF NORMAL ELEMENTS) 7 *-DISTRIBUTIONS (GENERAL
CASE) 13 EXERCISES 15 LECTURE 2. A CASE STUDY OF NON-NORMAL DISTRIBUTION
19 DESCRIPTION OF THE EXAMPLE 19 DYCK PATHS 22 THE DISTRIBUTION OF A +
A* 26 USING THE CAUCHY TRANSFORM 30 EXERCISES 33 LECTURE 3.
C*-PROBABILITY SPACES 35 FUNCTIONAL CALCULUS IN A C*-ALGEBRA 35
C*-PROBABILITY SPACES 39 *-DISTRIBUTION, NORM AND SPECTRUM FOR A NORMAL
ELEMENT 43 EXERCISES 46 LECTURE 4. NON-COMMUTATIVE JOINT DISTRIBUTIONS *
49 JOINT DISTRIBUTIONS * 49 JOINT ^-DISTRIBUTIONS 53 JOINT
*-DISTRIBUTIONS AND ISOMORPHISM 55 EXERCISES 59 LECTURE 5. DEFINITION
AND BASIC PROPERTIES OF FREE INDEPENDENCE 63 THE CLASSICAL SITUATION:
TENSOR INDEPENDENCE * 63 DEFINITION OF FREE INDEPENDENCE 64 THE EXAMPLE
OF A FREE PRODUCT OF GROUPS 66 FREE INDEPENDENCE AND JOINT MOMENTS 69
SOME BASIC PROPERTIES OF FREE INDEPENDENCE 71 ARE THERE OTHER UNIVERSAL
PRODUCT CONSTRUCTIONS? 75 VIII CONTENTS EXERCISES 78 LECTURE 6. FREE
PRODUCT OF *-PROBABILITY SPACES 81 FREE PRODUCT OF UNITAL ALGEBRAS 81
FREE PRODUCT OF NON-COMMUTATIVE PROBABILITY SPACES 84 FREE PRODUCT OF
*-PROBABILITY SPACES 86 EXERCISES 92 LECTURE 7. FREE PRODUCT OF
C*-PROBABILITY SPACES 95 THE GNS REPRESENTATION 95 FREE PRODUCT OF
C*-PROBABILITY SPACES 99 EXAMPLE: SEMICIRCULAR SYSTEMS AND THE FULL FOCK
SPACE 102 EXERCISES 109 PART 2. CUMULANTS 113 LECTURE 8. MOTIVATION:
FREE CENTRAL LIMIT THEOREM 115 CONVERGENCE IN DISTRIBUTION 115 GENERAL
CENTRAL LIMIT THEOREM 117 CLASSICAL CENTRAL LIMIT THEOREM 120 FREE
CENTRAL LIMIT THEOREM 121 THE MULTI-DIMENSIONAL CASE 125 CONCLUSION AND
OUTLOOK 131 EXERCISES 132 LECTURE 9. BASIC COMBINATORICS I: NON-CROSSING
PARTITIONS 135 NON-CROSSING PARTITIONS OF AN ORDERED SET 135 THE LATTICE
STRUCTURE OF NC(N) 144 THE FACTORIZATION OF INTERVALS IN NC 14 8
EXERCISES 153 LECTURE 10. BASIC COMBINATORICS II: MOBIUS INVERSION 155
CONVOLUTION IN THE FRAMEWORK OF A POSET 155 MOBIUS INVERSION IN A
LATTICE 160 THE MOBIUS FUNCTION OF NC 162 MULTIPLICATIVE FUNCTIONS ON NC
164 FUNCTIONAL EQUATION FOR CONVOLUTION WITH /X N 168 EXERCISES , 171
LECTURE 11. FREE CUMULANTS: DEFINITION AND BASIC PROPERTIES 173
MULTIPLICATIVE FUNCTIONALS ON NC 173 DEFINITION OF FREE CUMULANTS 175
PRODUCTS AS ARGUMENTS 178 FREE INDEPENDENCE AND FREE CUMULANTS 182
CONTENTS IX CUMULANTS OF RANDOM VARIABLES 185 EXAMPLE: SEMICIRCULAR AND
CIRCULAR ELEMENTS 187 EVEN ELEMENTS 188 APPENDIX: CLASSICAL CUMULANTS
190 EXERCISES 193 LECTURE 12. SUMS OF FREE RANDOM VARIABLES 195 FREE
CONVOLUTION 195 ANALYTIC CALCULATION OF FREE CONVOLUTION 200 PROOF OF
THE FREE CENTRAL LIMIT THEOREM VIA 7?.-TRANSFORM 202 FREE POISSON
DISTRIBUTION 203 COMPOUND FREE POISSON DISTRIBUTION 206 EXERCISES 208
LECTURE 13. MORE ABOUT LIMIT THEOREMS AND INFINITELY DIVISIBLE
DISTRIBUTIONS 211 LIMIT THEOREM FOR TRIANGULAR ARRAYS 211 CUMULANTS OF
OPERATORS ON FOCK SPACE 214 INFINITELY DIVISIBLE DISTRIBUTIONS 215
CONDITIONALLY POSITIVE DEFINITE SEQUENCES 216 CHARACTERIZATION OF
INFINITELY DIVISIBLE DISTRIBUTIONS 220 EXERCISES 221 LECTURE 14.
PRODUCTS OF FREE RANDOM VARIABLES 223 MULTIPLICATIVE FREE CONVOLUTION
223 COMBINATORIAL DESCRIPTION OF FREE MULTIPLICATION 225 COMPRESSION BY
A FREE PROJECTION 228 CONVOLUTION SEMIGROUPS (N M )T I 231 COMPRESSION
BY A FREE FAMILY OF MATRIX UNITS 233 EXERCISES 236 LECTURE 15.
I?-DIAGONAL ELEMENTS % 237 MOTIVATION: CUMULANTS OF HAAR UNITARY
ELEMENTS \ 237 DEFINITION OF I?-DIAGONAL ELEMENTS 240 SPECIAL
REALIZATIONS OF TRACIAL I?-DIAGONAL ELEMENTS 245 PRODUCT OF TWO FREE
EVEN ELEMENTS 249 THE FREE ANTI-COMMUTATOR OF EVEN ELEMENTS 251 POWERS
OF I?-DIAGONAL ELEMENTS * 253 EXERCISES 254 PART 3. TRANSFORMS AND
MODELS 257 LECTURE 16. THE ^-TRANSFORM 259 THE MULTI-VARIABLE
I?-TRANSFORM 259 X CONTENTS THE FUNCTIONAL EQUATION FOR THE -R-TRANSFORM
265 MORE ABOUT THE ONE-DIMENSIONAL CASE 269 EXERCISES 272 LECTURE 17.
THE OPERATION OF BOXED CONVOLUTION 273 THE DEFINITION OF BOXED
CONVOLUTION, AND ITS MOTIVATION 273 BASIC PROPERTIES OF BOXED
CONVOLUTION 275 RADIAL SERIES 277 THE MOBIUS SERIES AND ITS USE 280
EXERCISES 285 LECTURE 18. MORE ON THE ONE-DIMENSIONAL BOXED CONVOLUTION
287 RELATION TO MULTIPLICATIVE FUNCTIONS ON NC 287 THE 5-TRANSFORM 293
EXERCISES 300 LECTURE 19. THE FREE COMMUTATOR 303 FREE COMMUTATORS OF
EVEN ELEMENTS 303 FREE COMMUTATORS IN THE GENERAL CASE 310 THE
CANCELATION PHENOMENON 314 EXERCISES - 317 LECTURE 20. I?-CYCLIC
MATRICES 321 DEFINITION AND EXAMPLES OF /^-CYCLIC MATRICES 321 THE
CONVOLUTION FORMULA FOR AN /^-CYCLIC MATRIX 324 I?-CYCLIC FAMILIES OF
MATRICES 329 APPLICATIONS OF THE CONVOLUTION FORMULA 331 EXERCISES 335
LECTURE 21. THE FULL FOCK SPACE MODEL FOR THE I?-TRANSFORM 339
DESCRIPTION OF THE FOCK SPACE MODEL 339 AN APPLICATION: REVISITING FREE
COMPRESSIONS 346 EXERCISES 356 LECTURE 22. GAUSSIAN RANDOM MATRICES 359
MOMENTS OF GAUSSIAN RANDOM VARIABLES 359 RANDOM MATRICES IN GENERAL 361
SELFADJOINT GAUSSIAN RANDOM MATRICES AND GENUS EXPANSION 363 ASYMPTOTIC
FREE INDEPENDENCE FOR SEVERAL INDEPENDENT GAUSSIAN RANDOM MATRICES 368
ASYMPTOTIC FREE INDEPENDENCE BETWEEN GAUSSIAN RANDOM MATRICES AND
CONSTANT MATRICES 371 LECTURE 23. UNITARY RANDOM MATRICES 379 HAAR
UNITARY RANDOM MATRICES 379 CONTENTS XI THE LENGTH FUNCTION ON
PERMUTATIONS 381 ASYMPTOTIC FREENESS FOR HAAR UNITARY RANDOM MATRICES
384 ASYMPTOTIC FREENESS BETWEEN RANDOMLY ROTATED CONSTANT MATRICES 385
EMBEDDING OF NON-CROSSING PARTITIONS INTO PERMUTATIONS 390 EXERCISES
,393 NOTES AND COMMENTS 395 REFERENCES 405 INDEX 411 |
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| author | Nica, Alexandru Speicher, Roland 1960- |
| author_GND | (DE-588)111876451 |
| author_facet | Nica, Alexandru Speicher, Roland 1960- |
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| author_sort | Nica, Alexandru |
| author_variant | a n an r s rs |
| building | Verbundindex |
| bvnumber | BV021741276 |
| callnumber-first | Q - Science |
| callnumber-label | QA164 |
| callnumber-raw | QA164 |
| callnumber-search | QA164 |
| callnumber-sort | QA 3164 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 320 SK 600 SK 620 |
| ctrlnum | (OCoLC)244813737 (DE-599)BVBBV021741276 |
| dewey-full | 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 |
| dewey-search | 512.55 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV021741276 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:29:29Z |
| indexdate | 2024-07-09T20:42:58Z |
| institution | BVB |
| isbn | 9780521858526 0521858526 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014954631 |
| oclc_num | 244813737 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-824 DE-29T DE-634 DE-188 DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-824 DE-29T DE-634 DE-188 DE-11 |
| physical | XV, 417 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Cambrigde Univ. Press |
| record_format | marc |
| series | London Mathematical Society lecture notes series |
| series2 | London Mathematical Society lecture notes series |
| spelling | Nica, Alexandru Verfasser aut Lectures on the combinatorics of free probability Alexandru Nica ; Roland Speicher 1. publ. Cambridge [u.a.] Cambrigde Univ. Press 2006 XV, 417 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture notes series 335 Algèbres d'opérateurs ram Analyse combinatoire Matrices aléatoires ram Probabilités ram Théorie des probabilités libres Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Kombinatorische Analysis (DE-588)4164746-4 s Speicher, Roland 1960- Verfasser (DE-588)111876451 aut London Mathematical Society lecture notes series 335 (DE-604)BV000000130 335 http://www.loc.gov/catdir/enhancements/fy0703/2006299523-d.html Beschreibung für Leser http://www.loc.gov/catdir/enhancements/fy0703/2006299523-t.html Inhaltsverzeichnis GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014954631&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nica, Alexandru Speicher, Roland 1960- Lectures on the combinatorics of free probability London Mathematical Society lecture notes series Algèbres d'opérateurs ram Analyse combinatoire Matrices aléatoires ram Probabilités ram Théorie des probabilités libres Kombinatorische Analysis (DE-588)4164746-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4164746-4 (DE-588)4079013-7 |
| title | Lectures on the combinatorics of free probability |
| title_auth | Lectures on the combinatorics of free probability |
| title_exact_search | Lectures on the combinatorics of free probability |
| title_exact_search_txtP | Lectures on the combinatorics of free probability |
| title_full | Lectures on the combinatorics of free probability Alexandru Nica ; Roland Speicher |
| title_fullStr | Lectures on the combinatorics of free probability Alexandru Nica ; Roland Speicher |
| title_full_unstemmed | Lectures on the combinatorics of free probability Alexandru Nica ; Roland Speicher |
| title_short | Lectures on the combinatorics of free probability |
| title_sort | lectures on the combinatorics of free probability |
| topic | Algèbres d'opérateurs ram Analyse combinatoire Matrices aléatoires ram Probabilités ram Théorie des probabilités libres Kombinatorische Analysis (DE-588)4164746-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Algèbres d'opérateurs Analyse combinatoire Matrices aléatoires Probabilités Théorie des probabilités libres Kombinatorische Analysis Wahrscheinlichkeitstheorie |
| url | http://www.loc.gov/catdir/enhancements/fy0703/2006299523-d.html http://www.loc.gov/catdir/enhancements/fy0703/2006299523-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014954631&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000130 |
| work_keys_str_mv | AT nicaalexandru lecturesonthecombinatoricsoffreeprobability AT speicherroland lecturesonthecombinatoricsoffreeprobability |
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