Geometry of isotropic convex bodies

著者

• Brazitikos, Silouanos

書誌事項

Geometry of isotropic convex bodies

Silouanos Brazitikos ... [et al.]

（Mathematical surveys and monographs, v. 196）

American Mathematical Society, c2014

注記

Includes bibliographical references (p. 565-583) and index

内容説明・目次

内容説明

The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalisation, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin-shell conjecture and the Kannan-Lovasz-Simonovits conjecture. This book provides a self-contained and up to date account of the progress that has been made in the last fifteen years.

目次

Background from asymptotic convex geometry Isotropic log-concave measures Hyperplane conjecture and Bourgain's upper bound Partial answers L q -centroid bodies and concentration of mass Bodies with maximal isotropic constant Logarithmic Laplace transform and the isomorphic slicing problem Tail estimates for linear functionals M and M? *-estimates Approximating the covariance matrix Random polytopes in isotropic convex bodies Central limit problem and the thin shell conjecture The thin shell estimate Kannan-Lovasz-Simonovits conjecture Infimum convolution inequalities and concentration Information theory and the hyperplane conjecture Bibliography Subject index Author index

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詳細情報

• NII書誌ID(NCID): BB15527026
• ISBN:
  • 9781470414566
• LCCN: 2013041914
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: xx, 594 p.
• 大きさ: 26 cm
• 分類:
  • LCC : QA331.5
  • DC23 : 516.3/62
• 件名:
  • LCSH : Convex geometry
  • LCSH : Banach lattices
• 親書誌ID:
  • BA00134419