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      Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical System

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          Abstract

          Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are described by infinite measure dynamical systems.We show that the time average of the observation function which is not the \(L^1(m)\) function, whose average with respect to the invariant measure \(m\) is finite, converges to the generalized arcsine distribution. This result leads to the novel view that the correlation function is intrinsically random and does not decay. Moreover, it is also numerically shown that the time average of the observation function converges to the stable distribution when the observation function has the infinite mean.

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          Fluorescence intermittency in single cadmium selenide nanocrystals

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            Proof of the Ergodic Theorem.

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              The Rayleigh-Bénard Instability and the Evolution of Turbulence

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                Author and article information

                Journal
                09 January 2008
                Article
                10.1007/s10955-008-9544-9
                0801.1382
                Custom metadata
                J. Stat. Phys. 132 (2008) 171-186
                8 pages, 8 figures
                cond-mat.stat-mech

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