000			02812cam a2200289 i 4500
001			135869
003			ISI Library, Kolkata
005			20150617112820.0
008			131028s2014 riu b 001 0 eng
020			_a9781470414566 (alk. paper)
040			_aISI Library
082	0	0	_a510MS _223 _bAm512
100	1		_aBrazitikos, Silouanos.
245	1	0	_aGeometry of isotropic convex bodies / _cSilouanos Brazitikos...[et al.].
260			_aProvidence : _bAmerican Mathematical Society, _cc2014.
300			_axx, 594 p. ; _c27 cm.
490	0		_aMathematical surveys and monographs ; _vv 196.
504			_aIncludes bibliographical references (pages 565-583) and indexes.
505	0		_a1. Background from asymptotic convex geometry-- 2. Isotropic log-concave measures-- 3. Hyperplane conjecture and Bourgain's upper bound-- 4. Partial answers-- 5. Lq-centroid bodies and concentration of mass-- 6. Bodies with maximal isotropic constant-- 7. Logarithmic laplace transform and the isomorphic-- 8. Tail estimates for linear functionals-- 9. M and M*-estimates-- 10. Approximating the covariance matrix-- 11. Random polytopes in isotropic convex bodies-- 12. Central limit problem and the thin shell conjecture-- 13. The thin shell estimate-- 14. Kannan-Lovasz-Simonovits conjecture-- 15. Infimum convolution inequalities and concentration-- 16. Information theory and the hyperplane conjecture-- Bibliography-- Subject index-- Author index.
520			_aThe 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.
650		0	_aConvex geometry.
650		0	_aBanach lattices.
700	1		_aGiannopoulos, Apostolos.
700	1		_aValettas, Petros.
700	1		_aVritsiou, Beatrice-Helen.
942			_2ddc _cBK
999			_c419030 _d419030