Geometry of Isotropic Convex Bodies
American Mathematical Society (Verlag)
978-1-4704-1456-6 (ISBN)
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.
Silouanos Brazitikos, University of Athens, Greece. Apostolos Giannopoulos, University of Athens, Greece. Petros Valettas, Texas A & M University, College Station, TX. Beatrice-Helen Vritsiou, University of Athens, Greece.
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-Lovász-Simonovits conjecture
Infimum convolution inequalities and concentration
Information theory and the hyperplane conjecture
Bibliography
Subject index
Author index
Erscheint lt. Verlag | 30.5.2014 |
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Reihe/Serie | Mathematical Surveys and Monographs |
Verlagsort | Providence |
Sprache | englisch |
Maße | 178 x 254 mm |
Gewicht | 1225 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 1-4704-1456-2 / 1470414562 |
ISBN-13 | 978-1-4704-1456-6 / 9781470414566 |
Zustand | Neuware |
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