03702nam 22007455 450 991074695140332120240628103857.03-031-26300-610.1007/978-3-031-26300-2(MiAaPQ)EBC30764562(Au-PeEL)EBL30764562(DE-He213)978-3-031-26300-2(PPN)272733946(CKB)28443813500041(EXLCZ)992844381350004120230930d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierGeometric Aspects of Functional Analysis Israel Seminar (GAFA) 2020-2022 /edited by Ronen Eldan, Bo'az Klartag, Alexander Litvak, Emanuel Milman1st ed. 2023.Cham :Springer International Publishing :Imprint: Springer,2023.1 online resource (443 pages)Lecture Notes in Mathematics,1617-9692 ;2327Print version: Eldan, Ronen Geometric Aspects of Functional Analysis Cham : Springer International Publishing AG,c2023 9783031262999 This 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.Lecture Notes in Mathematics,1617-9692 ;2327Functional analysisConvex geometryDiscrete geometryProbabilitiesFunctional AnalysisConvex and Discrete GeometryProbability TheoryAnàlisi funcionalthubGeometria analíticathubLlibres electrònicsthubFunctional analysis.Convex geometry.Discrete geometry.Probabilities.Functional Analysis.Convex and Discrete Geometry.Probability Theory.Anàlisi funcionalGeometria analítica515.7515.7Eldan Ronen1430868Klartag Bo'az477682Litvak Alexander1430869Milman Emanuel739651Eldan Ronen1430868Klartag Bo'az477682Litvak Alexander1430869Milman Emanuel739651MiAaPQMiAaPQMiAaPQBOOK9910746951403321Geometric Aspects of Functional Analysis3570867UNINA