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Distribution of a tagged particle position in the one-dimensional symmetric simple exclusion process with two-sided Bernoulli initial condition. (English) Zbl 1482.60126

Summary: For the two-sided Bernoulli initial condition with density \(\rho_-\) (resp. \( \rho_+\)) to the left (resp. to the right), we study the distribution of a tagged particle in the one dimensional symmetric simple exclusion process. We obtain a formula for the moment generating function of the associated current in terms of a Fredholm determinant. Our arguments are based on a combination of techniques from integrable probability which have been developed recently for studying the asymmetric exclusion process and a subsequent intricate symmetric limit. An expression for the large deviation function of the tagged particle position is obtained, including the case of the stationary measure with uniform density \(\rho \).

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C22 Interacting particle systems in time-dependent statistical mechanics
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