### 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) |
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Pages (from-to) | 54-92 |

Number of pages | 39 |

Journal | Israel Journal of Mathematics |

Volume | 21 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1975 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Israel Journal of Mathematics*,

*21*(1), 54-92. https://doi.org/10.1007/BF02757134

**The central limit theorem for Carleman's equation.** / McKean, H. P.

Research output: Contribution to journal › Article

*Israel Journal of Mathematics*, vol. 21, no. 1, pp. 54-92. https://doi.org/10.1007/BF02757134

}

TY - JOUR

T1 - The central limit theorem for Carleman's equation

AU - McKean, H. P.

PY - 1975/3

Y1 - 1975/3

N2 - 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)′.

AB - 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)′.

UR - http://www.scopus.com/inward/record.url?scp=51249192577&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249192577&partnerID=8YFLogxK

U2 - 10.1007/BF02757134

DO - 10.1007/BF02757134

M3 - Article

VL - 21

SP - 54

EP - 92

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 1

ER -