Geometruc aspects of functional analysis : Israel seminar (GAFA) 2020-2022 / Ronen Eldan, Bo'az Klartag, Alexander Litvak, Emanuel Milman, editors.
2023
QA320
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Title
Geometruc aspects of functional analysis : Israel seminar (GAFA) 2020-2022 / Ronen Eldan, Bo'az Klartag, Alexander Litvak, Emanuel Milman, editors.
ISBN
9783031263002 (electronic bk.)
3031263006 (electronic bk.)
3031262999
9783031262999
3031263006 (electronic bk.)
3031262999
9783031262999
Published
Cham, Switzerland : Springer, 2023.
Language
English
Description
1 online resource (360 pages) : illustrations (black and white).
Item Number
10.1007/978-3-031-26300-2 doi
Call Number
QA320
Dewey Decimal Classification
515/.7
Summary
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.
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Description based on print version record.
Added Author
Eldan, Ronen, editor.
Klartag, Bo'az, editor.
Litvak, Alexander, editor.
Milman, Emanuel, 1977- editor.
Klartag, Bo'az, editor.
Litvak, Alexander, editor.
Milman, Emanuel, 1977- editor.
Series
Lecture notes in mathematics (Springer-Verlag) ; 2327.
Available in Other Form
GEOMETRIC ASPECTS OF FUNCTIONAL ANALYSIS.
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