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We study the fluctuations of the current J(t) of the totally asymmetricexclusion process with open boundaries. Using a density matrix renormalizationgroup approach, we calculate the cumulant generating function of the current.This function can be interpreted as a free energy for an ensemble in whichhistories are weighted by exp(-sJ(t)). We show that in this ensemble the modelhas a first order space-time phase transition at s=0. We numerically determinethe finite size scaling of the cumulant generating function near this phasetransition, both in the non-equilibrium steady state and for large times.

Finite size scaling of current fluctuations in the totally asymmetric exclusion process