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A CLASS OF GROWTH MODELS RESCALING TO KPZ

Part of: Miscellaneous topics - Partial differential equations Stochastic analysis Time-dependent statistical mechanics (dynamic and nonequilibrium)

Published online by Cambridge University Press:  19 November 2018

MARTIN HAIRER  and
JEREMY QUASTEL
MARTIN HAIRER
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK; m.hairer@imperial.ac.uk
JEREMY QUASTEL
Affiliation:
Department of Mathematics, University of Toronto, M5S 1L2, Canada; quastel@math.toronto.edu

Abstract

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We consider a large class of $1+1$-dimensional continuous interface growth models and we show that, in both the weakly asymmetric and the intermediate disorder regimes, these models converge to Hopf–Cole solutions to the KPZ equation.

MSC classification

Primary: 60H15: Stochastic partial differential equations
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations 82C28: Dynamic renormalization group methods
Type
Research Article
Information
Forum of Mathematics, Pi , Volume 6 , 2018 , e3
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2018

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