Globally coupled chaos violates the law of large numbers but not the central-limit theorem

Kunihiko Kaneko
Phys. Rev. Lett. 65, 1391 – Published 17 September 1990; Erratum Phys. Rev. Lett. 66, 243 (1991)
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Abstract

The title statement is numerically shown for a globally coupled chaotic system. With an increasing number of elements, N, the distribution of the mean field approaches a Gaussian distribution, but the decrease of its mean-square deviation with N stops for large N. This violation of the law of large numbers is found to be caused by the emergence of a subtle coherence among elements, as is measured by the mutual information. With the inclusion of noise, the law of large numbers is restored. The mean-square deviation decreases in proportion to Nβ with an exponent β<1 depending on the noise strength.

  • Received 18 June 1990

DOI:https://doi.org/10.1103/PhysRevLett.65.1391

©1990 American Physical Society

Erratum

Authors & Affiliations

Kunihiko Kaneko

  • Institute of Physics, College of Arts and Sciences, The University of Tokyo, Komaba, Meguro-ku, Tokyo 153, Japan

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Issue

Vol. 65, Iss. 12 — 17 September 1990

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