Itai Benjamini, Vincent Tassion
Published 2015-05-22Version 1
We show that a superposition of an $\varepsilon$-Bernoulli bond percolation and any everywhere percolating subgraph of $\mathbb Z^d$, $d\ge 2$, results in a connected subgraph, which after a renormalization dominates supercritical Bernoulli percolation. This result, which confirms a conjecture of the first author together with H\"aggstr\"om and Schramm (2000), is mainly motivated by obtaining finite volume characterizations of uniqueness for general percolation processes.
On the Ornstein-Zernike behaviour for the Bernoulli bond percolation on $\mathbb{Z}^{d},d\geq3,$ in the supercitical regime
Max-linear models on infinte graphs generated by Bernoulli bond percolation
A remark on monotonicity in Bernoulli bond Percolation
![QR code for arXiv:1505.06069 [math.PR]](http://oss.arxitics.com/images/favicon.svg)