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We calculate the first four cumulants of the integrated current of the onedimensional symmetric simple exclusion process of $N$ sites with open boundaryconditions. For large system size $N$, the generating function of theintegrated current depends on the densities $\rho_a$ and $\rho_b$ of the tworeservoirs and on the fugacity $z$, the parameter conjugated to the integratedcurrent, through a single parameter. Based on our expressions for these firstfour cumulants, we make a conjecture which leads to a prediction for all thehigher cumulants. In the case $\rho_a=1$ and $\rho_b=0$, our conjecture givesthe same universal distribution as the one obtained by Lee, Levitov andYakovets for one dimensional quantum conductors in the metallic regime.Comment: submitted to Journal of Statistical Physic

Current Fluctuations in the One-Dimensional Symmetric Exclusion Process with Open Boundaries