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On Some Problems Concerning Log-Concave Random Vectors

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Convexity and Concentration

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 161))

Abstract

A Radon measure μ on a locally convex linear space F is called logarithmically concave (log-concave in short) if for any compact nonempty sets K, L ⊂ F and λ ∈ [0, 1], μ(λ K + (1 −λ)L) ≥ μ(K)λ μ(L)1−λ. A random vector with values in F is called log-concave if its distribution is logarithmically concave.

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Acknowledgements

This research was supported by the National Science Centre, Poland grant 2015/18/A/ST1/00553.

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Authors and Affiliations

  1. Institute of Mathematics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland

    Rafał Latała

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  1. Rafał Latała
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Correspondence to Rafał Latała .

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Editors and Affiliations

  1. Department of Mathematics, Rutgers University, Piscataway, New Jersey, USA

    Eric Carlen

  2. Department of Mathematical Sciences, University of Delaware, Newark, Delaware, USA

    Mokshay Madiman

  3. Department of Mathematics, Case Western Reserve University, Cleveland, Ohio, USA

    Elisabeth M. Werner

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Latała, R. (2017). On Some Problems Concerning Log-Concave Random Vectors. In: Carlen, E., Madiman, M., Werner, E. (eds) Convexity and Concentration. The IMA Volumes in Mathematics and its Applications, vol 161. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7005-6_16

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