Analytical and Probabilistic Methods in the Geomet

About the book:

The study of finite-dimensional Banach spaces and high-dimensional convex bodies has become a natural counterpart and complement to the classical functional analysis. Some powerful methods have been invented for this purpose since the 1970s, and many of them involve the ingenious use of probabilistic or functional inequalities. This book contains two series of lecture notes. The first of them explores the wide family of concentration inequalities and the way in which they can be applied in the geometry of convex bodies, while the second one discusses the notion of duality and tools coming from harmonic analysis. They lead the reader from classical results to recent advances in the subject.