The concentration of measure phenomenon:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, RI
AMS
2001
|
| Schriftenreihe: | Mathematical surveys and monographs
89 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009585732&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Umfang: | X, 179 S. |
| ISBN: | 0821828649 |
Internformat
MARC
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| 245 | 1 | 0 | |a The concentration of measure phenomenon |c Michel Ledoux |
| 264 | 1 | |a Providence, RI |b AMS |c 2001 | |
| 300 | |a X, 179 S. | ||
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| 490 | 1 | |a Mathematical surveys and monographs |v 89 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009585732 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 600f 2001 A 22401 |
|---|---|
| DE-BY-TUM_katkey | 1438889 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020104094 |
| _version_ | 1821932580499357696 |
| adam_text | CONTENTS
INTRODUCTION vii
1. CONCENTRATION FUNCTIONS
AND INEQUALITIES 1
1.1 First examples 1
1.2 Concentration functions 3
1.3 Deviation inequalities 5
1.4 Observable diameter 14
1.5 Expansion coefficient 15
1.6 Laplace bounds and infimum convolutions 16
Notes and Remarks 21
2. ISOPERIMETRIC AND FUNCTIONAL EXAMPLES 23
2.1 Isoperimetric examples 23
2.2 Brunn Minkowski inequalities 32
2.3 Semigroup tools 38
Notes and Remarks 44
3. CONCENTRATION AND GEOMETRY 47
3.1 Spectrum and concentration 47
3.2 Spectral and diameter bounds 53
3.3 Levy families 55
3.4 Topological applications 57
3.5 Euclidean sections of conyex bodies 60
Notes and Remarks 65
4. CONCENTRATION IN PRODUCT SPACES 67
4.1 Martingale methods 67
4.2 Convex hull approximation 72
4.3 Control by several points 79
4.4 Convex infimum convolution 82
4.5 The exponential distribution 83
Notes and Remarks 89
5. ENTROPY AND CONCENTRATION 91
5.1 Logarithmic Sobolev inequalities and concentration 91
5.2 Product measures 97
5.3 Modified logarithmic Sobolev inequalities 101
5.4 Discrete settings 108
V
vi CONTENTS
5.5 Covariance identities 114
Notes and Remarks 115
6. TRANSPORTATION COST INEQUALITIES 117
6.1 Information inequalities and concentration 117
6.2 Quadratic transportation cost inequalities 122
6.3 Transportation for product and non product measures 126
Notes and Remarks 132
7. SHARP BOUNDS ON GAUSSIAN
AND EMPIRICAL PROCESSES 133
7.1 Gaussian processes 133
7.2 Bounds on empirical processes 138
7.3 Sharper bounds via the entropic method 142
Notes and Remarks 149
8. SELECTED APPLICATIONS 151
8.1 Concentration of harmonic measures 151
8.2 Concentration for independent permutations 155
8.3 Subsequences, percolation, assignment 159
8.4 The spin glass free energy 163
8.5 Concentration of random matrices 167
Notes and Remarks 170
REFERENCES 171
INDEX 181
|
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| author_GND | (DE-588)112924360 |
| author_facet | Ledoux, Michel 1958- |
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| author_sort | Ledoux, Michel 1958- |
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| classification_tum | MAT 280f MAT 600f |
| ctrlnum | (OCoLC)248763209 (DE-599)BVBBV014002088 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014002088 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:57:23Z |
| institution | BVB |
| isbn | 0821828649 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009585732 |
| oclc_num | 248763209 |
| open_access_boolean | |
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| physical | X, 179 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | AMS |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spellingShingle | Ledoux, Michel 1958- The concentration of measure phenomenon Mathematical surveys and monographs Maßtheorie - Wahrscheinlichkeitstheorie - Konzentrationsmaß Maßtheorie (DE-588)4074626-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Konzentrationsmaß (DE-588)4165217-4 gnd |
| subject_GND | (DE-588)4074626-4 (DE-588)4079013-7 (DE-588)4165217-4 |
| title | The concentration of measure phenomenon |
| title_auth | The concentration of measure phenomenon |
| title_exact_search | The concentration of measure phenomenon |
| title_full | The concentration of measure phenomenon Michel Ledoux |
| title_fullStr | The concentration of measure phenomenon Michel Ledoux |
| title_full_unstemmed | The concentration of measure phenomenon Michel Ledoux |
| title_short | The concentration of measure phenomenon |
| title_sort | the concentration of measure phenomenon |
| topic | Maßtheorie - Wahrscheinlichkeitstheorie - Konzentrationsmaß Maßtheorie (DE-588)4074626-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Konzentrationsmaß (DE-588)4165217-4 gnd |
| topic_facet | Maßtheorie - Wahrscheinlichkeitstheorie - Konzentrationsmaß Maßtheorie Wahrscheinlichkeitstheorie Konzentrationsmaß |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009585732&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT ledouxmichel theconcentrationofmeasurephenomenon |
Inhaltsverzeichnis
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 600f 2001 A 22401 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |