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Convergence of the KMP model to the KPZ equation

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arxiv 2507.19222 v2 pith:FCXN7QOH submitted 2025-07-25 math.PR cond-mat.stat-mechmath-phmath.MP

Guillaume Barraquand , Francesco Casini This is my paper · ORCID
classification math.PRcond-mat.stat-mechmath-phmath.MP
keywords randomequationconvergenceenvironmentmodelprocessallowsapply
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The critical KPZ scale for the Averaging Process

    math.PR 2026-07 conditional novelty 8.0 of 10

    The averaging process has KPZ critical scale λ=7/8 rather than the moment-criterion value 3/4, with tilted fields converging to the multiplicative SHE of noise 1/√2.

  2. Random walks in Dirichlet random environment in dimension $d+1$

    cond-mat.stat-mech 2026-07 conditional novelty 6.0 of 10

    For random walks in a Dirichlet random environment, rare-trajectory fluctuations match KPZ exponents in d=1,2, and in d=3 an exact second-moment calculation bounds the disorder transition at v_c ≥ 0.639.

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