高斯过程的撒粉解耦不等式及其应用
A sprinkled decoupling inequality for Gaussian processes and applications
AI总结：
本文建立高斯向量递增事件的撒粉解耦不等式，并据此证明一类弱相关高斯场在 Z^d 与 R^d 上的渗流相变非平凡，纳入非平稳场和单色随机波等新情形。
摘要：
我们针对高斯向量的递增事件建立了一种撒粉解耦不等式，其误差仅取决于最大两两相关性。作为应用，我们证明了在 Z^d 或 R^d 上满足以下条件的高斯场的渗流相变非平凡性：（i）局部上确界一致有界；（ii）相关性随距离至少以指数 γ>3 的多对数速度衰减。这扩展了现有相变非平凡性结果的适用范围，涵盖了非平稳场和单色随机波等新例子。
英文摘要：
We establish a sprinkled decoupling inequality for increasing events of Gaussian vectors with an error that depends only on the maximum pairwise correlation. As an application we prove the non-triviality of the percolation phase transition for Gaussian fields on $\mathbb{Z}^d$ or $\mathbb{R}^d$ with (i) uniformly bounded local suprema, and (ii) correlations which decay at least polylogarithmically in the distance with exponent $γ> 3$; this expands the scope of existing results on non-triviality of the phase transition, covering new examples such as non-stationary fields and monochromatic random waves.
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