Geometry and probability
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 292-310 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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
Mots-clés : normal distribution.
@article{TVP_2017_62_2_a3,
     author = {V. A. Zorich},
     title = {Geometry and probability},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {292--310},
     year = {2017},
     volume = {62},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a3/}
}
TY  - JOUR
AU  - V. A. Zorich
TI  - Geometry and probability
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2017
SP  - 292
EP  - 310
VL  - 62
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a3/
LA  - ru
ID  - TVP_2017_62_2_a3
ER  - 
%0 Journal Article
%A V. A. Zorich
%T Geometry and probability
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2017
%P 292-310
%V 62
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a3/
%G ru
%F TVP_2017_62_2_a3
V. A. Zorich. Geometry and probability. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 292-310. http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a3/

[1] Kolmogorov, v. 2, Etikh strok beguschikh tesma..., Yubileinoe izd. v 3-kh kn., ed. A. N. Shiryaev, Fizmatlit, M., 2003, 672 pp. | Zbl

[2] V. A. Zorich, “Multidimensional geometry, functions of very many variables, and probability”, Theory Probab. Appl., 59:3 (2015), 481–493 | DOI | DOI | MR | Zbl

[3] M. Gromov, “Appendix I. Isoperimetric inequality in Riemannian manifolds”: V. D. Milman, G. Schechtman, Asymptotic theory of finite dimensional normed spaces, Lecture Notes in Math., 1200, Berlin, Springer-Verlag, 1986, 114–129 | DOI | MR | Zbl

[4] K. Ball, “An elementary introduction to modern convex geometry”, Flavors of geometry, Math. Sci. Res. Inst. Publ., 31, Cambridge Univ. Press, Cambridge, 1997, 1–58 | MR | Zbl

[5] V. D. Milman, “Geometrization of probability”, Geometry and dynamics of groups and spaces, Progr. Math., 265, Birkhäuser, Basel, 2008, 647–667 | DOI | MR | Zbl

[6] M. L. Gromov, “Colourful categories”, Russian Math. Surveys, 70:4 (2015), 591–655 | DOI | DOI | MR | Zbl

[7] I. M. Gel'fand, M. I. Graev, N. Ya. Vilenkin, Generalized functions, v. 5, Integral geometry and representation theory, Academic Press, New York–London, 1966, xvii+449 pp. | MR | MR | Zbl | Zbl

[8] Ya. G. Sinai, Theory of phase transitions: rigorous results, International Series in Natural Philosophy, 108, Pergamon Press, Oxford–Elmsford, N.Y., 1982, viii+150 pp. | MR | MR | Zbl | Zbl

[9] Ya. G. Sinai, Topics in ergodic theory, Princeton Math. Ser., 44, Princeton Univ. Press, Princeton, NJ, 1994, viii+218 pp. | MR | Zbl | Zbl

[10] Ya. G. Sinai, Selecta, v. I, Ergodic theory and dynamical systems, Springer, New York, 2010, xvi+496 pp. | MR | Zbl

[11] Ya. G. Sinai, Selecta, v. II, Probability theory, statistical mechanics, mathematical physics and mathematical fluid dynamics, Springer, New York, 2010, xxii+514 pp. | MR | Zbl

[12] S. Smirnov, “Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits”, C. R. Acad. Sci. Paris Sér. I Math., 333:3 (2001), 239–244 | DOI | MR | Zbl

[13] H. Kesten, “The work of Stanislav Smirnov”, Proceedings of the International Congress of Mathematicians (Hyderabad, August 19–27, 2010), v. 1, Hindustan Book Agency, New Delhi, 2010, 73–84 | MR | Zbl