Open Access
2019 Quantitative homogenization of the disordered $\nabla \phi $ model
Paul Dario
Electron. J. Probab. 24: 1-99 (2019). DOI: 10.1214/19-EJP347


We study the $\nabla \phi $ model with uniformly convex Hamiltonian $\mathcal{H} (\phi ) := \sum V(\nabla \phi )$ and prove a quantitative rate of convergence for the finite-volume surface tension as well as a quantitative rate estimate for the $L^{2}$-norm for the field subject to affine boundary condition. One of our motivations is to develop a new toolbox for studying this problem that does not rely on the Helffer-Sjöstrand representation. Instead, we make use of the variational formulation of the partition function, the notion of displacement convexity from the theory of optimal transport, and the recently developed theory of quantitative stochastic homogenization.


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Paul Dario. "Quantitative homogenization of the disordered $\nabla \phi $ model." Electron. J. Probab. 24 1 - 99, 2019.


Received: 7 November 2018; Accepted: 23 July 2019; Published: 2019
First available in Project Euclid: 10 September 2019

zbMATH: 07107397
MathSciNet: MR4003143
Digital Object Identifier: 10.1214/19-EJP347

Primary: 35B27 , 60K35 , 82B24

Keywords: Stochastic homogenization , Stochastic interface model

Vol.24 • 2019
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