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arXiv · 2507.19222

Convergence of the KMP model to the KPZ equation

Guillaume Barraquand·Francesco Casini
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Abstract

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 arXiv:2401.06073 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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Guillaume Barraquand, Francesco Casini. 2025-07-25. Convergence of the KMP model to the KPZ equation. https://arxiv.org/abs/2507.19222

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