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Teor. Veroyatnost. i Primenen., 2017, Volume 62, Issue 2, Pages 292–310 (Mi tvp5109)  

This article is cited in 3 scientific papers (total in 4 papers)

Geometry and probability

V. A. Zorich

Lomonosov Moscow State University

Abstract: The present paper is chiefly based on the report delivered by the author on March 16, 2016 at the Principle Seminar of the Department of Probability held at the Faculty of Mechanics and Mathematics of Moscow State University. We describe in general terms the relations of the theory of probability with integral geometry and with the phenomenon of measure concentration in multidimensional geometry. In this context, we also discuss one general observation by A. N. Kolmogorov about the Gauss normal distribution, which was brought to the author's attention by A. N. Shiryaev.

Keywords: probability, integral geometry, multidimensional geometry, concentration of the measure, laws of large numbers, normal distribution.

DOI: https://doi.org/10.4213/tvp5109

Full text: PDF file (410 kB)
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English version:
Theory of Probability and its Applications, 2018, 62:2, 236–251

Bibliographic databases:

Received: 17.04.2016
Accepted:20.10.2016

Citation: V. A. Zorich, “Geometry and probability”, Teor. Veroyatnost. i Primenen., 62:2 (2017), 292–310; Theory Probab. Appl., 62:2 (2018), 236–251

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Aptekarev, V. M. Buchstaber, V. A. Vassiliev, M. L. Gromov, Yu. S. Ilyashenko, B. S. Kashin, V. M. Keselman, V. V. Kozlov, M. L. Kontsevich, I. M. Krichever, N. G. Kruzhilin, S. K. Lando, Yu. I. Manin, G. A. Margulis, S. Yu. Nemirovski, S. P. Novikov, Yu. G. Reshetnyak, Ya. G. Sinai, S. P. Suetin, D. V. Treschev, D. B. Fuchs, A. G. Khovanskii, E. M. Chirka, A. S. Schwarz, A. N. Shiryaev, “Vladimir Antonovich Zorich (on his 80th birthday)”, Russian Math. Surveys, 73:5 (2018), 935–939  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. K. Alekseev, A. E. Bondarev, “Ispolzovanie ansamblya chislennykh reshenii dlya otsenki pogreshnostei usecheniya i approksimatsii”, Preprinty IPM im. M. V. Keldysha, 2019, 107, 24 pp.  mathnet  crossref
    3. V. A. Zorich, “A remark on the distribution of values for functions of a large number of variables”, Theory Probab. Appl., 64:4 (2020), 631–635  mathnet  crossref  crossref  isi  elib
    4. A. K. Alekseev, A. E. Bondarev, A. E. Kuvshinnikov, “On uncertainty quantification via the ensemble of independent numerical solutions”, J. Comput. Sci., 42 (2020), UNSP 101114  crossref  mathscinet  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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