Asymptotic geometric analysis Part II
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| Sprache: | English |
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Providence, Rhode Island
American Mathematical Society
[2021]
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| Schriftenreihe: | Mathematical surveys and monographs
volume 261 |
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Datensatz im Suchindex
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| adam_text | Contents Preface to Part II ix Preface to Part I xix Notation and background from asymptotic geometric analysis Chapter 1. Functional inequalities and concentration of measure 1.1. The Poincaré inequality 1.2. Cost induced transforms and concentration 1.3. Logarithmic Sobolev inequality 1.4. Further reading 1.5. Notes and remarks xxxiii 1 2 25 38 51 58 Isoperimetric constants of log-concave measures and related problems 67 Isotropic log-concave probability measures Kannan-Lovász-Simonovits conjecture Isoperimetric constants of log-concave probability measures Thin-shell estimates and the central limit theorem Variance problem and the slicing problem Stochastic localization and the KLS conjecture Further reading Notes and remarks 69 71 80 91 97 102 111 115 Chapter 3. Inequalities for Gaussian measures 3.1. Gaussian isoperimetric inequality 3.2. Ehrharďs inequality 3.3. Gaussian measure of dilates of centrally symmetric convex bodies 3.4. Gaussian correlation inequality 3.5. The B-theorem 3.6. Applications to discrepancy 3.7. Some technical results 3.8. Notes and remarks 121 123 133 139 142 151 157 163 178 Chapter 4. Volume inequalities 4.1. Rearrangement of functions 4.2. Brascamp-Lieb-Luttinger inequality 4.3. The original proof of the Brascamp-Lieb inequality 4.4. Multidimensional versions 4.5. Applications to convex geometry 4.6. Vaaler’s inequality and related results 185 187 189 194 197 203 216 Chapter 2. 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 2.7. 2.8.
CONTENTS vi 4.7. Stochastic dominance and geometricinequalities 4.8. Blaschke-Petkantschin formulas 4.9. Further reading 4.10. Notes and remarks Local theory of finite dimensional normed spaces: type and cotype 257 Type and cotype Operator norms Maurey’s lemma and duality ofentropy Spaces with bounded cotype Grothendieck’s inequality Factorization through a Hilbertspace and Kwapien’s theorem The complemented subspace problem Krivine’s theorem Maurey-Pisier theorem Stable type p and the dimension of subspaces Further reading Notes and remarks 227 231 236 246 Chapter 5. 5.1. 5.2. 5.3. 5.4. 5.5. 5.6. 5.7. 5.8. 5.9. 5.10. 5.11. 5.12. Chapter 6. Geometry of the Banach-Mazur compactum 6.1. Diameter of the Banach-Mazur compactum 6.2. Random orthogonal factorizations 6.3. Diameter of the compactum in the non-symmetric case 6.4. Banach-Mazur distance to the cube 6.5. Elton’s theorem 6.6. Spaces with maximal distance to Euclidean space 6.7. Alon-Milman theorem 6.8. Dvoretzky theorem: dependence on ε 6.9. Further reading 6.10. Notes and remarks 259 265 281 286 291 295 297 302 323 333 344 357 365 367 373 380 383 396 400 401 407 412 422 Chapter 7.1. 7.2. 7.3. 7.4. 7.5. 7.6. 7. Asymptotic convex geometry andclassical symmetrizations Random Minkowski symmetrizations Minkowski symmetrizations Steiner symmetrizations Spherical harmonics Almost isometric symmetrization Notes and remarks 429 431 443 452 465 471 475 Chapter 8.1. 8.2. 8.3. 8.4. 8.5. 8.6. 8.7. 8. Restricted invertibility and the Kadison-Singer problem Sparse approximations of graphs Interlacing polynomials Restricted
invertibility Proportional Dvoretzky-Rogers factorization The Kadison-Singer problem Further reading Notes and remarks 481 482 490 493 504 509 526 533
CONTENTS vii Chapter 9. Functionalization of Geometry 9.1. Extending convex geometry to the log-concave realm 9.2. Functional Duality 9.3. Functional forms of geometric inequalities 9.4. Notes and remarks 539 540 552 566 588 Bibliography 595 Subject Index 629 Author Index 639
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| discipline | Mathematik |
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| id | DE-604.BV047861574 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-24T09:11:01Z |
| institution | BVB |
| isbn | 9781470463601 1470463601 |
| language | English |
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| owner | DE-188 DE-739 DE-83 DE-11 |
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| physical | xxxvii, 645 Seiten Diagramme |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spellingShingle | Artstein-Avidan, Shiri 1978- Giannopoulos, Apostolos 1963- Milman, Vitali D. 1939- Asymptotic geometric analysis Mathematical surveys and monographs Funktionalanalysis (DE-588)4018916-8 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4020236-7 |
| title | Asymptotic geometric analysis |
| title_auth | Asymptotic geometric analysis |
| title_exact_search | Asymptotic geometric analysis |
| title_full | Asymptotic geometric analysis Part II Shiri Artstein-Avidan ; Apostolos Giannopoulos ; Vitali D. Milman |
| title_fullStr | Asymptotic geometric analysis Part II Shiri Artstein-Avidan ; Apostolos Giannopoulos ; Vitali D. Milman |
| title_full_unstemmed | Asymptotic geometric analysis Part II Shiri Artstein-Avidan ; Apostolos Giannopoulos ; Vitali D. Milman |
| title_short | Asymptotic geometric analysis |
| title_sort | asymptotic geometric analysis |
| topic | Funktionalanalysis (DE-588)4018916-8 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Funktionalanalysis Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033244171&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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