DECOUPLING INEQUALITIES FOR THE GINZBURG-LANDAU ∇ φ MODELS
DECOUPLING INEQUALITIES FOR THE GINZBURG-LANDAU ∇ φ MODELS
复制标题
解耦 GINZBURG-LANDAU ∇ φ 模型的不平等
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Pierre
中科院分区：
文献类型：
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作者：
Pierre
We consider a class of of massless gradient Gibbs measures, in dimension greater or equal to three, and prove a decoupling inequality for these fields. As a result, we obtain detailed information about their geometry, and the percolative and non-percolative phases of their level sets, thus generalizing results obtained in [24], to the non-Gaussian case. Inequalities of similar flavor have also been successfully used in the study of random interlacements [27], [21]. A crucial aspect is the development of a suitable sprinkling technique, which relies on a particular representation of the correlations in terms of a random walk in a dynamic random environment, due to Helffer and Sjöstrand. The sprinkling can be effectively implemented by studying the Dirichlet problem for the corresponding Poisson equation, and quantifiying in how far a change in boundary condition along a sufficiently “small” part of the boundary affects the solution. Our results allow for uniformly convex potentials, and extend to non-convex perturbations thereof. Department of Mathematics December 2016 University of California, Los Angeles 520, Portola Plaza, MS 6172 Los Angeles, CA 90095 rodriguez@math.ucla.edu
具有时间相关遍历简并权重的随机游走的淬火不变性原理
DOI：
10.1214/17-aop1186
发表时间：
2018
期刊：
arXiv: Probability
影响因子：
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作者：
S. Andres;A. Chiarini;J.-D. Deuschel;M. Slowik
通讯作者：
M. Slowik