AI 中文总结
研究二维相依渗流模型在临界状态有无无限连通分量问题，通过建立含单调性等假设的通用准则，可确保无无限连通分量，还能恢复高斯水平集渗流等经典模型的已知结果。
AI 中文摘要
我们建立了一个通用准则，确保一类广泛的二维相依渗流模型在临界状态下不存在无限连通分量。我们的假设包括单调性、平稳性和遍历性、正相关性、定量解耦条件、渗流参数的连续性以及极端情况下的平凡行为。作为应用，我们展示了该准则如何恢复经典相依渗流模型的已知结果，如高斯水平集渗流和布尔渗流。
英文摘要
We establish a general criterion ensuring the absence of infinite connected components at criticality for a broad class of two-dimensional dependent percolation models. Our assumptions include monotonicity, stationarity and ergodicity, positive association, a quantitative decoupling condition, continuity in the percolation parameter, and trivial behavior at the extremes. As application, we show how our criterion recovers known results for classical dependent percolation models, such as Gaussian level-set percolation and Boolean percolation.
Comments17 pages
