The central limit theorem for Carleman's equation

H. P. McKean

doi:10.1007/BF02757134

The central limit theorem for Carleman's equation

H. P. McKean

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The purpose of this paper is to discuss the analogy between the law of large numbers and the central limit theorem of classical probability theory on the one hand and the hydrodynamical approximations in the statistical mechanics of gases on the other. The chief illustration is provided by Carleman's model [2] for which the central limit approximation is a kind of non-linear Brownian motion regulated by ∂n/∂t=(n'/n)^′.

Original language	English (US)
Pages (from-to)	54-92
Number of pages	39
Journal	Israel Journal of Mathematics
Volume	21
Issue number	1
DOIs	https://doi.org/10.1007/BF02757134
State	Published - Mar 1975

ASJC Scopus subject areas

General Mathematics

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abstract = "The purpose of this paper is to discuss the analogy between the law of large numbers and the central limit theorem of classical probability theory on the one hand and the hydrodynamical approximations in the statistical mechanics of gases on the other. The chief illustration is provided by Carleman's model [2] for which the central limit approximation is a kind of non-linear Brownian motion regulated by ∂n/∂t=(n'/n)′.",

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The central limit theorem for Carleman's equation

Abstract

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