Geometry of Isotropic Convex Bodies

About this Title

Silouanos Brazitikos, University of Athens, Athens, Greece, Apostolos Giannopoulos, University of Athens, Athens, Greece, Petros Valettas, Texas A & M University, College Station, TX and Beatrice-Helen Vritsiou, University of Athens, Athens, Greece

Publication: Mathematical Surveys and Monographs
Publication Year 2014: Volume 196
ISBNs: 978-1-4704-1456-6 (print); 978-1-4704-1526-6 (online)
DOI: http://dx.doi.org/10.1090/surv/196
MathSciNet review: MR3185453
MSC: Primary 52-02; Secondary 28Axx, 46Bxx, 52Axx, 60D05

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Table of Contents

Front/Back Matter

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Chapters

• Chapter 1. Background from asymptotic convex geometry
• Chapter 2. Isotropic log-concave measures
• Chapter 3. Hyperplane conjecture and Bourgain’s upper bound
• Chapter 4. Partial answers
• Chapter 5. $L_q$-centroid bodies and concentration of mass
• Chapter 6. Bodies with maximal isotropic constant
• Chapter 7. Logarithmic Laplace transform and the isomorphic slicing problem
• Chapter 8. Tail estimates for linear functionals
• Chapter 9. $M$ and $M*$-estimates
• Chapter 10. Approximating the covariance matrix
• Chapter 11. Random polytopes in isotropic convex bodies
• Chapter 12. Central limit problem and the thin shell conjecture
• Chapter 13. The thin shell estimate
• Chapter 14. Kannan-Lovász-Simonovits conjecture
• Chapter 15. Infimum convolution inequalities and concentration
• Chapter 16. Information theory and the hyperplane conjecture

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