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 \(\rho \).

对于左侧为（\ rho _ + \）密度为\（\ rho _- \）（resp。\（\ rho _ + \））的双面伯努利初始条件，我们研究了标记粒子的分布一维对称简单排除过程。我们根据Fredholm行列式获得了关联电流的矩生成函数的公式。我们的论据基于可积概率技术的组合，这些技术是最近为研究非对称排除过程和随后的复杂对称极限而开发的。获得了带标记粒子位置的大偏差函数的表达式，包括具有均匀密度\（\ rho \）的静态测度的情况。