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The central limit theorem for Carleman’s equation

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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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Authors and Affiliations

  1. Courant Institute, New York University, New York, U.S.A.

    H. P. McKean

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  1. H. P. McKean
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Additional information

Research supported by the National Science Foundation under NSF Grant NSF-GP-37069X1.

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McKean, H.P. The central limit theorem for Carleman’s equation. Israel J. Math. 21, 54–92 (1975). https://doi.org/10.1007/BF02757134

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  • DOI: https://doi.org/10.1007/BF02757134

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