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Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition

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Abstract

For the symmetric simple exclusion process on an infinite line, we calculate exactly the fluctuations of the integrated current Q t during time t through the origin when, in the initial condition, the sites are occupied with density ρ a on the negative axis and with density ρ b on the positive axis. All the cumulants of Q t grow like \(\sqrt{t}\) . In the range where \(Q_{t}\sim \sqrt{t}\) , the decay exp [−Q 3 t /t] of the distribution of Q t is non-Gaussian. Our results are obtained using the Bethe ansatz and several identities derived recently by Tracy and Widom for exclusion processes on the infinite line.

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Authors and Affiliations

  1. Laboratoire de Physique Statistique, École Normale Supérieure, 24, rue Lhomond, 75231, Paris Cedex 05, France

    Bernard Derrida & Antoine Gerschenfeld

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  1. Bernard Derrida
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  2. Antoine Gerschenfeld
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Correspondence to Bernard Derrida.

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We acknowledge the support of the French Ministry of Education through the ANR BLAN07-2184264 grant.

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Derrida, B., Gerschenfeld, A. Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition. J Stat Phys 136, 1–15 (2009). https://doi.org/10.1007/s10955-009-9772-7

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