arXiv · 1502.03051
A new proof of the sharpness of the phase transition for Bernoulli percolation on $\mathbb Z^d$
Abstract
We provide a new proof of the sharpness of the phase transition for nearest-neighbour Bernoulli percolation. More precisely, we show that - for $p p_c$, the probability that the origin belongs to an infinite cluster satisfies the mean-field lower bound $θ(p)\ge\tfrac{p-p_c}{p(1-p_c)}$. This note presents the argument of \cite{DumTas15}, which is valid for long-range Bernoulli percolation (and for the Ising model) on arbitrary transitive graphs in the simpler framework of nearest-neighbour Bernoulli percolation on $\mathbb Z^d$.
Explore related subjects
Keep this discovery
Hugo Duminil-Copin, Vincent Tassion. 2015-02-10. A new proof of the sharpness of the phase transition for Bernoulli percolation on $\mathbb Z^d$. https://arxiv.org/abs/1502.03051
Cite the original work for its findings. Save a collection to share your selection of sources.