Current large deviation function for the open asymmetric simple   exclusion process
  We consider the one dimensional asymmetric exclusion process with particle injection and extraction at two boundaries. The model is known to exhibit four distinct phases in its stationary state. We analyze the current statistics at the first site in the low and high density phases. In the limit of infinite system size, we conjecture an exact expression for the current large deviation function. 
Jan de Gier and Fabian H. L. Essler
cond-mat.stat-mech