KP governs random growth off a 1-dimensional substrate

  title={KP governs random growth off a 1-dimensional substrate},
  author={Jeremy Quastel and Daniel Remenik},
  journal={Forum of Mathematics, Pi},
Abstract The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev–Petviashvili (KP) equation. This is derived algebraically from a Fredholm determinant obtained in [MQR17] for the Kardar–Parisi–Zhang (KPZ) fixed point as the limit of the transition probabilities of TASEP, a special solvable model in the KPZ universality class. The Tracy–Widom distributions appear as special self-similar… 
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