The logarithmic derivative of the finite-dimensional distributions of the KPZ fixed point solves the matrix and scalar KP equation.
Solution of the Kolmogorov equation for TASEP
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abstract
We provide a direct and elementary proof that the formula obtained in [MQR17] for the TASEP transition probabilities for general (one-sided) initial data solves the Kolmogorov backward equation. The same method yields the solution for the related PushASEP particle system.
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KP governs random growth off a one dimensional substrate
The logarithmic derivative of the finite-dimensional distributions of the KPZ fixed point solves the matrix and scalar KP equation.