| Dewey Class |
515.7 |
| Title |
Geometric Aspects of Functional Analysis ([EBook]) : Israel Seminar (GAFA) 2020-2022 / edited by Ronen Eldan, Bo'az Klartag, Alexander Litvak, Emanuel Milman |
| Added Personal Name |
Eldan, Ronen |
| Klartag, Bo'az |
| Milman, Emanuel |
| Litvak, Alexander |
| Publication |
Cham : Springer International Publishing , 2023 |
| Physical Details |
: online resource (viii, 440 p., ill.) |
| Series |
Lecture Notes in Mathematics ; 2327 |
| ISBN |
9783031263002 |
| Summary Note |
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.(provided by publisher): |
| Mode of acces to digital resource |
Digital reproduction.- Cham : Springer International Publishing, 2023. - Digital book. Cham Springer Nature 2023. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
https://doi.org/10.1007/978-3-031-26300-2 |
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