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arXiv · 2509.01472

The non-perturbative sides of the Kardar-Parisi-Zhang equation

Léonie Canet
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Abstract

The Kardar-Parisi-Zhang (KPZ) equation is a celebrated non-linear stochastic dynamical equation yielding non-equilibrium universal scaling. It exhibits notorious non-perturbative aspects. The KPZ fixed point is strong-coupling, all the more in $d>1$. Strikingly, another, even stronger-coupling fixed point of the KPZ equation, called inviscid Burgers fixed point, has been recently unveiled. These non-pertubative features can be theoretically accessed and studied in a controlled way in all dimensions using the functional renormalisation group. We propose an overview of the related results, which provide a unified picture of the fixed-point structure and associated scaling regimes of the KPZ equation in $d=1$ and in higher dimensions.

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Léonie Canet. 2025-09-01. The non-perturbative sides of the Kardar-Parisi-Zhang equation. https://doi.org/10.1088/1742-5468%2Fae1e75

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