AI 中文总结
研究\(\mathbb{Z}^d\)上最近邻渗流模型相变的尖锐性，用OSSS不等式及改进方法证明，还对伯努利键渗流和位点渗流相结合的特殊情况做更广泛研究。
AI 中文摘要
我们证明了\(\mathbb{Z}^d\)上最近邻渗流模型相变的尖锐性，其中顶点具有独立类型，边的渗流概率取决于相邻顶点的类型。我们的证明使用了OSSS不等式，并将Duminil - Copin等人（2017年）为随机簇模型开发的方法应用于我们的设置。此外，我们对具有两个参数相变的伯努利键渗流和位点渗流相结合的特殊情况进行了更广泛的研究。
英文摘要
We show sharpness of the phase transition for a nearest-neighbour percolation model on $\mathbb Z^d$, where vertices carry independent types and the percolation probability of edges depends on the type of the adjacent vertices. Our proof uses the OSSS inequality and adapts to our setup the method developed in Duminil-Copin et al. (2017) for the random cluster model. Additionally, we provide a more extensive study of the special case of combined Bernoulli bond and site percolation featuring a phase transition with two parameters.
Comments18 pages, four figures
