Fluctuations of TASEP and LPP with general initial data
  We prove Airy process variational formulas for the one-point probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage percolation from a general lattice path to a point. We also consider variants of last passage percolation with inhomogeneous parameter geometric weights and provide variational formulas of a similar nature. This proves one aspect of the conjectural description of the renormalization fixed point of the Kardar-Parisi-Zhang universality class. 
Ivan Corwin, Zhipeng Liu, Dong Wang
math.PR cond-mat.stat-mech math-ph math.MP