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Springer Verlag, Journal of Statistical Physics, 1(136), p. 1-15

DOI: 10.1007/s10955-009-9772-7

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

Journal article published in 2009 by Bernard Derrida, Antoine Gerschenfeld
This paper is available in a repository.
This paper is available in a repository.

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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 $Q_t ∼ \sqrt{t}$, the decay $\exp [-Q_t^3/t]$ of the distribution of $Q_t$ is non-Gaussian. Our results are obtained using the Bethe ansatz and several identities recently derived by Tracy and Widom for exclusion processes on the infinite line. ; Comment: 2 figures