Renormalization of generalized KPZ equation

DOI10.1007/s10955-016-1636-3zbMath1369.82011arXiv1604.08712OpenAlexW2343508328MaRDI QIDQ526595

Matteo Marcozzi, Antti Kupiainen

Publication date: 15 May 2017

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.08712

zbMATH Keywords

regularizationrenormalization grouprandom fieldsKardar-Parisi-Zhang (KPZ) equationnonlinear stochastic PDEscaling and cutoffsstochastic hydrodynamics

Mathematics Subject Classification ID

Random fields (60G60) PDEs in connection with fluid mechanics (35Q35) Ill-posed problems for PDEs (35R25) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Renormalization group methods in equilibrium statistical mechanics (82B28) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Renormalization and other field-theoretical methods for turbulence (76F30)

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Cites Work

• Unnamed Item
• Renormalization group and stochastic PDEs
• Solving the KPZ equation
• A theory of regularity structures
• KAM theorem and quantum field theory
• Paracontrolled distributions and the 3-dimensional stochastic quantization equation
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Nonlinear fluctuations of weakly asymmetric interacting particle systems
• Wick polynomials and time-evolution of cumulants
• PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES
• The Malliavin Calculus and Related Topics
• Renormalization group and asymptotics of solutions of nonlinear parabolic equations