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arXiv · 1810.06131

Distribution of a tagged particle position in the one-dimensional symmetric simple exclusion process with two-sided Bernoulli initial condition

Takashi Imamura·Kirone Mallick·Tomohiro Sasamoto
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Abstract

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 $\rho$.

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Takashi Imamura, Kirone Mallick, Tomohiro Sasamoto. 2018-10-15. Distribution of a tagged particle position in the one-dimensional symmetric simple exclusion process with two-sided Bernoulli initial condition. https://arxiv.org/abs/1810.06131

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