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Teoriya Veroyatnostei i ee Primeneniya, 1976, Volume 21, Issue 1, Pages 63–80
(Mi tvp3275)
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This article is cited in 81 scientific papers (total in 82 papers)
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.
Received: 24.12.1974
Citation:
Ya. G. Sinaǐ, “Automodel probability distributions”, Teor. Veroyatnost. i Primenen., 21:1 (1976), 63–80; Theory Probab. Appl., 21:1 (1976), 64–80
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https://www.mathnet.ru/eng/tvp3275 https://www.mathnet.ru/eng/tvp/v21/i1/p63
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