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Flux Fluctuations in the One Dimensional Nearest Neighbors Symmetric Simple Exclusion Process

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Abstract

Let J(t) be the the integrated flux of particles in the symmetric simple exclusion process starting with the product invariant measure ν ρ with density ρ. We compute its rescaled asymptotic variance:

$$\mathop {\lim }\limits_{t \to \infty } t^{ - 1/2} \mathbb{V}J(t) = \sqrt {2/\pi } (1 - \rho )\rho$$

Furthermore we show that t −1/4 J(t) converges weakly to a centered normal random variable with this variance. From these results we compute the asymptotic variance of a tagged particle in the nearest neighbor case and show the corresponding central limit theorem.

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Authors and Affiliations

  1. Dipartimento di Matematica Pura ed Applicata, Università di L'Aquila, I-67100, L'Aquila, Italy

    A. De Masi

  2. IME USP, Caixa Postal 66281, 05315 970, São Paulo, São Paulo, Brazil

    P. A. Ferrari

Authors
  1. A. De Masi
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  2. P. A. Ferrari
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De Masi, A., Ferrari, P.A. Flux Fluctuations in the One Dimensional Nearest Neighbors Symmetric Simple Exclusion Process. Journal of Statistical Physics 107, 677–683 (2002). https://doi.org/10.1023/A:1014577928229

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