The Kardar-Parisi-Zhang equation as scaling limit of weakly asymmetric interacting Brownian motions

DOI10.1007/s00220-017-2918-6zbMath1378.60116arXiv1606.02331OpenAlexW3101611700MaRDI QIDQ2406834

Joscha Diehl, Nicolas Perkowski, Massimiliano Gubinelli

Publication date: 6 October 2017

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.02331

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05) Quasilinear parabolic equations (35K59)

Related Items (22)

Lectures on Energy Solutions for the Stationary KPZ Equation ⋮ \(\operatorname{ASEP}(q,j)\) converges to the KPZ equation ⋮ Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits ⋮ Derivation of the stochastic Burgers equation with Dirichlet boundary conditions from the WASEP ⋮ Stochastic Burgers equation from long range exclusion interactions ⋮ Stochastic PDE limit of the six vertex model ⋮ Space-time discrete KPZ equation ⋮ KPZ-type fluctuation exponents for interacting diffusions in equilibrium ⋮ Large scale limit of interface fluctuation models ⋮ Derivation of anomalous behavior from interacting oscillators in the high-temperature regime ⋮ Stationary directed polymers and energy solutions of the Burgers equation ⋮ HALF-SPACE MACDONALD PROCESSES ⋮ Some recent progress in singular stochastic partial differential equations ⋮ The infinitesimal generator of the stochastic Burgers equation ⋮ The KPZ limit of ASEP with boundary ⋮ Scaling of the sasamoto-Spohn model in equilibrium ⋮ Quadratic Fluctuations of the Simple Exclusion Process ⋮ The intermediate disorder regime for Brownian directed polymers in Poisson environment ⋮ Scaling limit of stationary coupled Sasamoto-Spohn models ⋮ Energy solutions of KPZ are unique ⋮ Derivation of the stochastic Burgers equation from totally asymmetric interacting particle systems ⋮ Universal break law for a class of models of polymer rupture

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