%0 Book Section %1 Milman2008 %A Milman, Vitali D. %B Geometry and Dynamics of Groups and Spaces: In Memory of Alexander Reznikov %C Basel %D 2008 %E Kapranov, Mikhail %E Manin, Yuri Ivanovich %E Moree, Pieter %E Kolyada, Sergiy %E Potyagailo, Leonid %I Birkhäuser Basel %K 2008 article geometry probability springer %P 647--667 %R 10.1007/978-3-7643-8608-5_15 %T Geometrization of Probability %U https://doi.org/10.1007/978-3-7643-8608-5_15 %X 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. %@ 978-3-7643-8608-5

@inbook{Milman2008, 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.}, added-at = {2018-06-17T13:53:44.000+0200}, address = {Basel}, author = {Milman, Vitali D.}, biburl = {https://www.bibsonomy.org/bibtex/210379217a5731392bdf876567da2208e/achakraborty}, booktitle = {Geometry and Dynamics of Groups and Spaces: In Memory of Alexander Reznikov}, description = {Geometrization of Probability | SpringerLink}, doi = {10.1007/978-3-7643-8608-5_15}, editor = {Kapranov, Mikhail and Manin, Yuri Ivanovich and Moree, Pieter and Kolyada, Sergiy and Potyagailo, Leonid}, interhash = {ffe693844dd9ea75e70c4958994ae49c}, intrahash = {10379217a5731392bdf876567da2208e}, isbn = {978-3-7643-8608-5}, keywords = {2008 article geometry probability springer}, pages = {647--667}, publisher = {Birkh{\"a}user Basel}, timestamp = {2018-06-17T13:53:44.000+0200}, title = {Geometrization of Probability}, url = {https://doi.org/10.1007/978-3-7643-8608-5_15}, year = 2008 }