Geometric Aspects of Functional Analysis: Israel Seminar (Gafa) 2020-2022
Eldan, Ronen, Klartag, Bo'az, Litvak, Alexander
- 出版商: Springer
- 出版日期: 2023-10-02
- 售價: $2,740
- 貴賓價: 9.5 折 $2,603
- 語言: 英文
- 頁數: 440
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031262999
- ISBN-13: 9783031262999
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商品描述
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.
商品描述(中文翻譯)
這本書反映了對功能分析幾何方面的研究的一般趨勢,其範圍廣泛。在巴拿赫空間的局部理論中,概率測度在高維度中的研究以及測度集中現象是一個經典主題。在這裡,這種現象從不同的角度進行了探討,包括通過對漢明立方體的分析,以及在薄殼和相關假設下對中心極限定理的定量估計。在本書中,經典的凸性理論起著核心作用,同時也研究了幾何不等式。這些不等式在某種程度上類似於布倫-明可夫斯基不等式,進一步揭示了凸性和歐幾里得空間的幾何性質。具有凸性或曲率特性的概率測度,如對數凹分佈,在高斯測度和歐幾里得空間中的熱流的非平凡性質的研究中佔據了同樣重要的地位。此外,還討論了這些思想與線性規劃和抽樣算法的相互作用,包括使用19世紀的經典凸性構造解決在線學習算法中的一個問題。