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We study the totally asymmetric exclusion process (TASEP) on a finiteone-dimensional lattice with open boundaries, i.e., in contact with tworeservoirs at different potentials. The total (time-integrated) current throughthe system is a random variable that scales linearly with time in the long timelimit. We give a parametric representation for the generating function of thecumulants of the current, which is related to the large deviation function byLaplace transform. This formula is valid for all system sizes and for allvalues of the boundary coupling parameters.

An Exact Formula for the Statistics of the Current in the TASEP with Open Boundaries