This article is cited in 2 scientific papers (total in 3 papers)
Automodel probability distributions
Ya. G. Sinaĭ
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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Theory of Probability and its Applications, 1976, 21:1, 64–80
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
\paper Automodel probability distributions
\jour Teor. Veroyatnost. i Primenen.
\jour Theory Probab. Appl.
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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
I. A. Kashapov, “Justification of the renormalization-group method”, Theoret. and Math. Phys., 42:2 (1980), 184–186
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
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