Convergence of the KMP model to the KPZ equation
Résumé
We prove that the Kipnis-Marchioro-Presutti (KMP) process converges to the Kardar-Parisi-Zhang (KPZ) equation, as time t goes to infinity, in a properly scaled observation window shifted by t 3/4 . Our proof is based on identifying the KMP process with a stochastic flow of kernels describing transition probabilities in a certain model of random walk in space-time random environment. This allows to apply a recent result of [Par24] proving convergence of the density field of random walks in random environment to the KPZ equation in a suitably general sense.
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