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Geometrization of Probability

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Geometry and Dynamics of Groups and Spaces

Part of the book series: Progress in Mathematics ((PM,volume 265))

Abstract

It was recently observed that asymptotic theory of high-dimensional convexity is extended in a very broad sense to the category of log-concave measures, and moreover, this extension is needed to understand and to solve some problems of asymptotic theory of high-dimensional convexity proper. Many important geometric inequalities were interpreted and extended to such category. On the other hand, some typical probabilisitic results are interpreted and proved in a geometric framework. Even more importantly, such extension to the log-concave category was needed to solve some central problems of a purely geometric nature. The goal of this article is to outline this development and to demonstrate examples of results which confirm this picture.

Supported in part by an Israel Science Foundation Grant and by the Minkowski Minerva Centre for Geometry.

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat-Aviv, Tel-Aviv, 69978, Israel

    Vitali D. Milman

Authors
  1. Vitali D. Milman
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Yale University, 10 Hillhouse Avenue, New Haven, CT, 06520, USA

    Mikhail Kapranov

  2. Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111, Bonn, Germany

    Yuri Ivanovich Manin  & Pieter Moree  & 

  3. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs’ka, 3, 01601, Kyiv, Ukraine

    Sergiy Kolyada

  4. UFR de Mathématiques, Université de Lille 1, 59655, Villeneuve d’Ascq Cedex, France

    Leonid Potyagailo

Additional information

Dedicated to the memory of Alexander (Sasha) Reznikov, a remarkable mathematician with tragic fate, and who called me his advisor, of which I was always proud.

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Milman, V.D. (2007). Geometrization of Probability. In: Kapranov, M., Manin, Y.I., Moree, P., Kolyada, S., Potyagailo, L. (eds) Geometry and Dynamics of Groups and Spaces. Progress in Mathematics, vol 265. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8608-5_15

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