LEADER 03470nam 22006615 450 001 996552469303316 005 20230930002832.0 010 $a3-031-26300-6 024 7 $a10.1007/978-3-031-26300-2 035 $a(MiAaPQ)EBC30764562 035 $a(Au-PeEL)EBL30764562 035 $a(DE-He213)978-3-031-26300-2 035 $a(PPN)272733946 035 $a(EXLCZ)9928443813500041 100 $a20230930d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric Aspects of Functional Analysis$b[electronic resource] $eIsrael Seminar (GAFA) 2020-2022 /$fedited by Ronen Eldan, Bo'az Klartag, Alexander Litvak, Emanuel Milman 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (443 pages) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2327 311 08$aPrint version: Eldan, Ronen Geometric Aspects of Functional Analysis Cham : Springer International Publishing AG,c2023 9783031262999 330 $aThis book reflects general trends in the study of geometric aspects of functional analysis, understood in a broad sense. A classical theme in the local theory of Banach spaces is the study of probability measures in high dimension and the concentration of measure phenomenon. Here this phenomenon is approached from different angles, including through analysis on the Hamming cube, and via quantitative estimates in the Central Limit Theorem under thin-shell and related assumptions. Classical convexity theory plays a central role in this volume, as well as the study of geometric inequalities. These inequalities, which are somewhat in spirit of the Brunn-Minkowski inequality, in turn shed light on convexity and on the geometry of Euclidean space. Probability measures with convexity or curvature properties, such as log-concave distributions, occupy an equally central role and arise in the study of Gaussian measures and non-trivial properties of the heat flow in Euclidean spaces. Also discussed are interactions of this circle of ideas with linear programming and sampling algorithms, including the solution of a question in online learning algorithms using a classical convexity construction from the 19th century. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2327 606 $aFunctional analysis 606 $aConvex geometry 606 $aDiscrete geometry 606 $aProbabilities 606 $aFunctional Analysis 606 $aConvex and Discrete Geometry 606 $aProbability Theory 615 0$aFunctional analysis. 615 0$aConvex geometry. 615 0$aDiscrete geometry. 615 0$aProbabilities. 615 14$aFunctional Analysis. 615 24$aConvex and Discrete Geometry. 615 24$aProbability Theory. 676 $a515.7 700 $aEldan$b Ronen$01430868 701 $aKlartag$b Bo'az$0477682 701 $aLitvak$b Alexander$01430869 701 $aMilman$b Emanuel$0739651 701 $aEldan$b Ronen$01430868 701 $aKlartag$b Bo'az$0477682 701 $aLitvak$b Alexander$01430869 701 $aMilman$b Emanuel$0739651 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996552469303316 996 $aGeometric Aspects of Functional Analysis$93570867 997 $aUNISA