MARC Record from marc_columbia

LEADER: 05633cam a2200613 i 4500
001 11602017
005 20220301084107.0
008 150805m20159999riua b 001 0 eng
010 $a 2014049152
035 $a(OCoLC)ocn919165916
040 $aDLC$beng$erda$cPUL$dOCLCO$dZCU$dOCLCQ$dRCE$dUAT$dCEF$dXFF$dFQG$dOCLCQ$dHUELT$dOCLCQ$dOCLCO$dYUS$dNHM$dVA@
019 $a920106998
020 $a9781470421939$q(pt. 1 ;$qalk. paper)
020 $a1470421933$q(pt. 1 ;$qalk. paper)
020 $a9781470463601$q(pt. 2 ; alk. paper)
020 $a1470463601$q(pt. 2$qalk. paper)
035 $a(OCoLC)919165916$z(OCoLC)920106998
042 $apcc
050 00 $aQA360$b.A78 2015
082 00 $a515/.1$223
084 $a52Axx$a46Bxx$a60Dxx$a28Axx$a46B20$a46B09$a52A20$a52A21$a52A23$a68-02$2msc
049 $aZCUA
100 1 $aArtstein-Avidan, Shiri,$d1978-$eauthor.
245 10 $aAsymptotic geometric analysis /$cShiri Artstein-Avidan, Apostolos Giannopoulos, Vitali D. Milman.
264 1 $aProvidence, Rhode Island :$bAmerican Mathematical Society,$c2015-
300 $avolumes :$billustrations ;$c27 cm
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
338 $avolume$bnc$2rdacarrier
490 1 $aMathematical surveys and monographs ;$vvolume 202, volume 261
504 $aIncludes bibliographical references and indexes.
520 $a"The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here ini a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality. The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more"--Back cover.
505 0 $a[Pt. 1] Convex bodies: classical geometric inequalities -- Classical positions of convex bodies -- Isomorphic isoperimetric inequalities and concentration of measure -- Metric entropy and covering numbers estimates -- Almost Euclidean subspaces of finite dimensional normed spaces -- The ℓ-position and the Rademacher projection -- Proportional Theory -- M-position and the reverse Brunn-Minkowski inequality -- Gaussian approach -- Volume distribution in convex bodies -- Appendix A: Elementary convexity -- Appendix B: Advanced convexity -- pt. 2. Functional inequalities and concentration of measure -- Isoperimetric constants of log-concave measures and related problems --Inequalities for Gaussian measures -- Volume inequalities --Local theory of finite dimensional normed spaces: type and cotype -- Geometry of the Banach-Mazur compactum -- Asymptotic convex geometry and classical symmetrizations -- Restricted invertibility and the Kadison-Singer problem -- Functionalization of geometry.
650 0 $aGeometric analysis.
650 0 $aFunctional analysis.
650 7 $aFunctional analysis.$2fast$0(OCoLC)fst00936061
650 7 $aGeometric analysis.$2fast$0(OCoLC)fst01747051
650 7 $aConvex and discrete geometry$xGeneral convexity$xGeneral convexity.$2msc
650 7 $aFunctional analysis$xNormed linear spaces and Banach spaces; Banach lattices$xNormed linear spaces and Banach spaces; Banach lattices.$2msc
650 7 $aProbability theory and stochastic processes$xGeometric probability and stochastic geometry$xGeometric probability and stochastic geometry.$2msc
650 7 $aMeasure and integration$xClassical measure theory$xClassical measure theory.$2msc
650 7 $aFunctional analysis$xNormed linear spaces and Banach spaces; Banach lattices$xGeometry and structure of normed linear spaces.$2msc
650 7 $aFunctional analysis$xNormed linear spaces and Banach spaces; Banach lattices$xProbabilistic methods in Banach space theory.$2msc
650 7 $aConvex and discrete geometry$xGeneral convexity$xConvex sets in $n$ dimensions (including convex hypersurfaces)$2msc
650 7 $aConvex and discrete geometry$xGeneral convexity$xFinite-dimensional Banach spaces (including special norms, zonoids, etc.)$2msc
650 7 $aConvex and discrete geometry$xGeneral convexity$xAsymptotic theory of convex bodies.$2msc
650 7 $aComputer science$xResearch exposition (monographs, survey articles)$2msc
700 1 $aGiannopoulos, Apostolos,$d1963-$eauthor.
700 1 $aMilman, Vitali D.,$d1939-$eauthor.
773 08 $g1$w(DE-604)BV042738629
773 08 $w(DE-604)BV042738629$g1
830 0 $aMathematical surveys and monographs ;$vno. 202, no. 261.
852 01 $bmat$hQA360$i.A78 2015
866 41 $80$apt.1-2