Geometry of isotropic convex bodies:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2014
|
| Series: | Mathematical surveys and monographs
196 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverz. S. 565 - 583 |
| Physical Description: | XX, 594 Seiten |
| ISBN: | 1470414562 9781470414566 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV041959333 | ||
| 003 | DE-604 | ||
| 005 | 20230824 | ||
| 007 | t | ||
| 008 | 140708s2014 |||| 00||| eng d | ||
| 020 | |a 1470414562 |9 1-4704-1456-2 | ||
| 020 | |a 9781470414566 |c hbk |9 978-1-4704-1456-6 | ||
| 035 | |a (OCoLC)882965502 | ||
| 035 | |a (DE-599)OBVAC11432056 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-19 |a DE-83 |a DE-739 |a DE-824 |a DE-20 |a DE-188 | ||
| 082 | 0 | |a 516.3/62 | |
| 084 | |a SK 380 |0 (DE-625)143235: |2 rvk | ||
| 084 | |a 44A10 |2 msc | ||
| 084 | |a 60D05 |2 Geometric probability, stochastic geometry, random sets | ||
| 084 | |a 52A23 |2 Asymptotic theory of convex bodies | ||
| 084 | |a 46B06 |2 msc | ||
| 084 | |a 52A23 |2 msc | ||
| 084 | |a 46B06 |2 Asymptotic theory of Banach spaces | ||
| 084 | |a 60D05 |2 msc | ||
| 084 | |a 31.59 |2 bkl | ||
| 084 | |a 52-02 |2 Research exposition (monographs, survey articles) | ||
| 084 | |a 44A10 |2 Laplace transform | ||
| 245 | 1 | 0 | |a Geometry of isotropic convex bodies |c Silouanos Brazitikos ; Apostolos Giannopoulos ; Petros Valettas ; Beatrice-Helen Vritsiou |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2014 | |
| 300 | |a XX, 594 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v 196 | |
| 500 | |a Literaturverz. S. 565 - 583 | ||
| 650 | 0 | 7 | |a Konvexe Geometrie |0 (DE-588)4407260-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Konvexe Geometrie |0 (DE-588)4407260-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Brazitikos, Silouanos |d 1990- |e Sonstige |0 (DE-588)1054173397 |4 oth | |
| 700 | 1 | |a Giannopoulos, Apostolos |d 1963- |e Sonstige |0 (DE-588)1074789954 |4 oth | |
| 700 | 1 | |a Valettas, Petros |d ca. 20./21. Jh. |e Sonstige |0 (DE-588)1294339923 |4 oth | |
| 700 | 1 | |a Vritsiou, Beatrice-Helen |d ca. 20./21. Jh. |e Sonstige |0 (DE-588)1294340328 |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1526-6 |
| 830 | 0 | |a Mathematical surveys and monographs |v 196 |w (DE-604)BV000018014 |9 196 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027402186&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027402186&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027402186 | |
Record in the Search Index
| _version_ | 1810687512819007488 |
|---|---|
| adam_text |
Contents
Preface
ix
Chapter
1.
Background from asymptotic convex geometry
1
1.1.
Convex bodies
1
1.2. Brunn—
Minkowski inequality
4
1.3.
Applications of the Brunn-Minkowski inequality
8
1.4.
Mixed volumes
12
1.5.
Classical positions of convex bodies
16
1.6.
Brascamp-Lieb inequality and its reverse form
22
1.7.
Concentration of measure
25
1.8.
Entropy estimates
34
1.9.
Gaussian and sub-Gaussian processes
38
1.10.
Dvoretzky type theorems
43
1.11.
The ¿'-position and Pisier's inequality
50
1.12.
Milman's low M*-estimate and the quotient of subspace theorem
52
1.13.
Bourgain-Milman inequality and the Af-position
55
1.14.
Notes and references
58
Chapter
2. Isotropie
log-concave measures
63
2.1.
Log-concave probability measures
63
2.2.
Inequalities for log-concave functions
66
2.3. Isotropie
log-concave measures
72
2.4.
фа
-estimates
78
2.5.
Convex bodies associated with log-concave functions
84
2.6.
Further reading
94
2.7.
Notes and references
100
Chapter
3. Hyperplane
conjecture and Bourgain's upper bound
103
3.1. Hyperplane
conjecture
104
3.2.
Geometry of
isotropie
convex bodies
108
3.3.
Bourgain's upper bound for the
isotropie
constant
116
3.4.
The
^з-саѕе
123
3.5.
Further reading
128
3.6.
Notes and references
134
Chapter
4.
Partial answers
139
4.1.
Unconditional convex bodies
139
4.2.
Classes with uniformly bounded
isotropie
constant
144
4.3.
The
isotropie
constant of
Schatten
classes
150
4.4.
Bodies with few vertices or few facets
155
vi
CONTENTS
4.5.
Further reading
161
4.6.
Notes and references
170
Chapter
5.
Lç-centroid
bodies and concentration of mass
173
5.1.
.Lq-centroid bodies
174
5.2.
Paouris' inequality
182
5.3.
Small ball probability estimates
190
5.4.
A short proof of Paouris' deviation inequality
197
5.5.
Further reading
202
5.6.
Notes and references
209
Chapter
6.
Bodies with maximal
isotropie
constant
213
6.1.
Symmetrization of
isotropie
convex bodies
214
6.2.
Reduction to bounded volume ratio
223
6.3.
Regular
isotropie
convex bodies
227
6.4.
Reduction to negative moments
231
6.5.
Reduction to h(K,Z°{K))
234
6.6.
Further reading
239
6.7.
Notes and references
242
Chapter
7.
Logarithmic Laplace transform and the isomorphic
slicing problem
243
7.1.
Klartag's first approach to the isomorphic slicing problem
244
7.2.
Logarithmic Laplace transform and convex perturbations
249
7.3.
Klartag's solution to the isomorphic slicing problem
251
7.4.
Isotropie
position and the reverse
Santaló
inequality
254
7.5.
Volume radius of the centroid bodies
256
7.6.
Notes and references
270
Chapter
8.
Tail estimates for linear functionals
271
8.1.
Covering numbers of the centroid bodies
273
8.2.
Volume radius of the
-02-body
284
8.3.
Distribution of the ^-norm
292
8.4.
Super-Gaussian directions
298
8.5.
фа
-estimates for marginals of
isotropie log-
concave measures
301
8.6.
Further reading
304
8.7.
Notes and references
310
Chapter
9.
M
and M* -estimates
313
9.1.
Mean width in the
isotropie case
313
9.2.
Estimates for M{K) in the
isotropie case
322
9.3.
Further reading
330
9.4.
Notes and references
332
Chapter
10.
Approximating the covariance matrix
333
10.1.
Optimal estimate
334
10.2.
Further reading
349
10.3.
Notes and references
354
Chapter
11.
Random polytopes in
isotropie
convex bodies
357
11.1.
Lower bound for the expected volume radius
358
CONTENTS
vii
11.2.
Linear number of points
363
11.3.
Asymptotic shape
367
11.4.
Isotropie
constant
377
11.5.
Further reading
381
11.6.
Notes and references
387
Chapter
12.
Central limit problem and the thin shell conjecture
389
12.1.
From the thin shell estimate to Gaussian marginals
391
12.2.
The log-concave case
397
12.3.
The thin shell conjecture
402
12.4.
The thin shell conjecture in the unconditional case
407
12.5.
Thin shell conjecture and the
hyperplane
conjecture
415
12.6.
Notes and references
422
Chapter
13.
The thin shell estimate
425
13.1.
The method of proof and Fleury's estimate
427
13.2.
The thin shell estimate of
Guédon
and E. Milman
436
13.3.
Notes and references
458
Chapter
14.
Kannan-Lovász-Simonovits
conjecture
461
14.1.
Isoperimetric constants for log-concave probability measures
462
14.2.
Equivalence of the isoperimetric constants
473
14.3.
Stability of the Cheeger constant
477
14.4.
The conjecture and the first lower bounds
480
14.5.
Poincaré
constant in the unconditional case
485
14.6.
KLS-conjecture and the thin shell conjecture
486
14.7.
Further reading
505
14.8.
Notes and references
509
Chapter
15.
Infìmum
convolution inequalities and concentration
511
15.1.
Property
(τ)
512
15.2.
Infimum convolution conjecture
523
15.3.
Concentration inequalities
527
15.4.
Comparison of weak and strong moments
533
15.5.
Further reading
535
15.6.
Notes and references
546
Chapter
16.
Information theory and the
hyperplane
conjecture
549
16.1.
Entropy gap and the
isotropie
constant
550
16.2.
Entropy jumps for log-concave random vectors with spectral gap
552
16.3.
Further reading
559
16.4.
Notes and references
562
Bibliography
565
Subject Index
585
Author Index
591
: '■^TÍ-Vl/JUv —
;;■
;: :^
and the local theory of Banach
^ i •■í^spaceš; Itísi^síy
'tíjösely
ІйШо.т^
as probability theory partial,
;·'γ:
:7';|ШшїйЩ
^ and combinatorics.
·:'
Λ.
it^iśnow
üriderstood ihat
thewiivexity
assumption ^forces most of the volume-of a.
;Ц:
"/vMgh-limeîişion^
ΠΠΟ-
>.
".'V
■ "'
naiÉré:
ЩОЩ
therö
;
ше
the
¿І|Ш^рйф1ейі>
the:f
hin
shell conjecture and the
Kannan»"
; .
Lóvász^Siffi^
5
tíeif-conUiined
and up to date
.\;;ir
·;■
а(ХО!№{.оМіг рш
yeaľs,
.;■-■■■■· |
| any_adam_object | 1 |
| author_GND | (DE-588)1054173397 (DE-588)1074789954 (DE-588)1294339923 (DE-588)1294340328 |
| building | Verbundindex |
| bvnumber | BV041959333 |
| classification_rvk | SK 380 |
| ctrlnum | (OCoLC)882965502 (DE-599)OBVAC11432056 |
| dewey-full | 516.3/62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/62 |
| dewey-search | 516.3/62 |
| dewey-sort | 3516.3 262 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV041959333</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230824</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">140708s2014 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1470414562</subfield><subfield code="9">1-4704-1456-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781470414566</subfield><subfield code="c">hbk</subfield><subfield code="9">978-1-4704-1456-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)882965502</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)OBVAC11432056</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.3/62</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 380</subfield><subfield code="0">(DE-625)143235:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">44A10</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60D05</subfield><subfield code="2">Geometric probability, stochastic geometry, random sets</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">52A23</subfield><subfield code="2">Asymptotic theory of convex bodies</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">46B06</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">52A23</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">46B06</subfield><subfield code="2">Asymptotic theory of Banach spaces</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60D05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.59</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">52-02</subfield><subfield code="2">Research exposition (monographs, survey articles)</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">44A10</subfield><subfield code="2">Laplace transform</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Geometry of isotropic convex bodies</subfield><subfield code="c">Silouanos Brazitikos ; Apostolos Giannopoulos ; Petros Valettas ; Beatrice-Helen Vritsiou</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Math. Soc.</subfield><subfield code="c">2014</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XX, 594 Seiten</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Mathematical surveys and monographs</subfield><subfield code="v">196</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 565 - 583</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konvexe Geometrie</subfield><subfield code="0">(DE-588)4407260-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Konvexe Geometrie</subfield><subfield code="0">(DE-588)4407260-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Brazitikos, Silouanos</subfield><subfield code="d">1990-</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)1054173397</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Giannopoulos, Apostolos</subfield><subfield code="d">1963-</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)1074789954</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Valettas, Petros</subfield><subfield code="d">ca. 20./21. Jh.</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)1294339923</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Vritsiou, Beatrice-Helen</subfield><subfield code="d">ca. 20./21. Jh.</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)1294340328</subfield><subfield code="4">oth</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4704-1526-6</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematical surveys and monographs</subfield><subfield code="v">196</subfield><subfield code="w">(DE-604)BV000018014</subfield><subfield code="9">196</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Passau - ADAM Catalogue Enrichment</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027402186&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Passau - ADAM Catalogue Enrichment</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027402186&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Klappentext</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027402186</subfield></datafield></record></collection> |
| id | DE-604.BV041959333 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-20T04:22:55Z |
| institution | BVB |
| isbn | 1470414562 9781470414566 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027402186 |
| oclc_num | 882965502 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-83 DE-739 DE-824 DE-20 DE-188 |
| owner_facet | DE-19 DE-BY-UBM DE-83 DE-739 DE-824 DE-20 DE-188 |
| physical | XX, 594 Seiten |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Geometry of isotropic convex bodies Silouanos Brazitikos ; Apostolos Giannopoulos ; Petros Valettas ; Beatrice-Helen Vritsiou Providence, RI American Math. Soc. 2014 XX, 594 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 196 Literaturverz. S. 565 - 583 Konvexe Geometrie (DE-588)4407260-0 gnd rswk-swf Konvexe Geometrie (DE-588)4407260-0 s DE-604 Brazitikos, Silouanos 1990- Sonstige (DE-588)1054173397 oth Giannopoulos, Apostolos 1963- Sonstige (DE-588)1074789954 oth Valettas, Petros ca. 20./21. Jh. Sonstige (DE-588)1294339923 oth Vritsiou, Beatrice-Helen ca. 20./21. Jh. Sonstige (DE-588)1294340328 oth Erscheint auch als Online-Ausgabe 978-1-4704-1526-6 Mathematical surveys and monographs 196 (DE-604)BV000018014 196 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=027402186&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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=027402186&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Geometry of isotropic convex bodies Mathematical surveys and monographs Konvexe Geometrie (DE-588)4407260-0 gnd |
| subject_GND | (DE-588)4407260-0 |
| title | Geometry of isotropic convex bodies |
| title_auth | Geometry of isotropic convex bodies |
| title_exact_search | Geometry of isotropic convex bodies |
| title_full | Geometry of isotropic convex bodies Silouanos Brazitikos ; Apostolos Giannopoulos ; Petros Valettas ; Beatrice-Helen Vritsiou |
| title_fullStr | Geometry of isotropic convex bodies Silouanos Brazitikos ; Apostolos Giannopoulos ; Petros Valettas ; Beatrice-Helen Vritsiou |
| title_full_unstemmed | Geometry of isotropic convex bodies Silouanos Brazitikos ; Apostolos Giannopoulos ; Petros Valettas ; Beatrice-Helen Vritsiou |
| title_short | Geometry of isotropic convex bodies |
| title_sort | geometry of isotropic convex bodies |
| topic | Konvexe Geometrie (DE-588)4407260-0 gnd |
| topic_facet | Konvexe Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027402186&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027402186&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT brazitikossilouanos geometryofisotropicconvexbodies AT giannopoulosapostolos geometryofisotropicconvexbodies AT valettaspetros geometryofisotropicconvexbodies AT vritsioubeatricehelen geometryofisotropicconvexbodies |