Let $G$ be a connected, locally finite, transitive graph, and consider Bernoulli bond percolation on $G$. We prove that if $G$ is nonamenable and $p > p_c(G)$ then there exists a positive constant $c_p$ such that \[\mathbf{P}_p(n \leq |K| < \infty) \leq e^{-c_p n}\] for every $n\geq 1$, where $K$ is the cluster of the origin. We deduce the following two corollaries: 1. Every infinite cluster in supercritical percolation on a transitive nonamenable graph has anchored expansion almost surely. This answers positively a question of Benjamini, Lyons, and Schramm (1997). 2. For transitive nonamenable graphs, various observables including the percolation probability, the truncated susceptibility, and the truncated two-point function are analytic functions of $p$ throughout the entire supercritical phase.

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不可命名图上的超临界渗透：等周测量、分析性和簇大小分布的指数衰减

令 $G$ 是一个连通的、局部有限的、可传递的图，并考虑在 $G$ 上的伯努利债券渗透。我们证明如果 $G$ 是不可命名的并且 $p > p_c(G)$ 那么存在一个正常数 $c_p$ 使得 \[\mathbf{P}_p(n \leq |K| < \infty) \leq e^{-c_p n}\] 对于每个 $n\geq 1$，其中 $K$ 是原点的簇。我们推导出以下两个推论： 1. 传递不可命名图上超临界渗透中的每个无限簇几乎肯定锚定了扩展。这肯定地回答了 Benjamini、Lyons 和 Schramm (1997) 的问题。2. 对于传递不可命名图，在整个超临界相中，包括渗透概率、截断敏感性和截断两点函数在内的各种可观察量都是 $p$ 的解析函数。