Fluctuations of the solutions to the KPZ equation in dimensions three and higher
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DOI: 10.1007/s00440-019-00938-w
Abstract: We prove, using probabilistic techniques and analysis on the Wiener space, that the large scale fluctuations of the KPZ equation in $$d\ge 3$$ d ≥ 3 with a small coupling constant, driven by a white… read more here.
Keywords: solutions kpz; kpz equation; dimensions three; fluctuations solutions ... See more keywords
The Scaling Limit of the KPZ Equation in Space Dimension 3 and Higher
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DOI: 10.1007/s10955-018-2014-0
Abstract: We study in the present article the Kardar–Parisi–Zhang (KPZ) equation $$\begin{aligned} \partial _t h(t,x)=\nu \Delta h(t,x)+\lambda |\nabla h(t,x)|^2 +\sqrt{D}\, \eta (t,x), \qquad (t,x)\in \mathbb {R}_+\times \mathbb {R}^d \end{aligned}$$∂th(t,x)=νΔh(t,x)+λ|∇h(t,x)|2+Dη(t,x),(t,x)∈R+×Rdin $$d\ge 3$$d≥3 dimensions in the perturbative regime,… read more here.
Keywords: lambda; space; scaling limit; kpz equation ... See more keywords
Solution of the 1D KPZ Equation by Explicit Methods
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DOI: 10.3390/sym14040699
Abstract: The Kardar–Parisi-Zhang (KPZ) equation is examined using the recently published leapfrog–hopscotch (LH) method as well as the most standard forward time centered space (FTCS) scheme and the Heun method. The methods are verified by reproducing… read more here.
Keywords: solution kpz; equation; kpz equation; equation explicit ... See more keywords