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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1976, Volume 21, Issue 1, Pages 63–80 (Mi tvp3275)

Automodel probability distributions

Ya. G. Sinaĭ

Moscow

Abstract: As in traditional probability theory, one of the most difficult problems in the theory of phase transitions concerns the limit distributions for sums of a large number of random variables. However, these variables are strongly dependent. Therefore the usual methods cannot be applied. The limit distributions which appear in these problems are invariant under a subgroup of linear endomorphisms, called the renormalization group.
In this paper, we find Gaussian invariant distributions and construct formal series for non-Gaussian ones. Our approach is inspired by the famous renormalization group method widely known in physical literature and developed mainly by K. Wilson, M. Fisher and L. Kadanoff.

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English version:
Theory of Probability and its Applications, 1976, 21:1, 64–80

Bibliographic databases:

Citation: Ya. G. Sinaǐ, “Automodel probability distributions”, Teor. Veroyatnost. i Primenen., 21:1 (1976), 63–80; Theory Probab. Appl., 21:1 (1976), 64–80

Citation in format AMSBIB
\Bibitem{Sin76} \by Ya.~G.~Sina{\v\i} \paper Automodel probability distributions \jour Teor. Veroyatnost. i Primenen. \yr 1976 \vol 21 \issue 1 \pages 63--80 \mathnet{http://mi.mathnet.ru/tvp3275} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=407959} \zmath{https://zbmath.org/?q=an:0358.60031} \transl \jour Theory Probab. Appl. \yr 1976 \vol 21 \issue 1 \pages 64--80 \crossref{https://doi.org/10.1137/1121005} 

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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. L. V. Bogachev, “Distribution of the total spin in the spherical model with long-range potential”, Theoret. and Math. Phys., 34:3 (1978), 247–255
2. I. A. Kashapov, “Justification of the renormalization-group method”, Theoret. and Math. Phys., 42:2 (1980), 184–186
3. S. P. Novikov, L. A. Bunimovich, A. M. Vershik, B. M. Gurevich, E. I. Dinaburg, G. A. Margulis, V. I. Oseledets, S. A. Pirogov, K. M. Khanin, N. N. Chentsova, “Yakov Grigor'evich Sinai (on his sixtieth birthday)”, Russian Math. Surveys, 51:4 (1996), 765–778