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arXiv · 1902.03207

Upper bounds on the percolation correlation length

Hugo Duminil-Copin·Gady Kozma·Vincent Tassion
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Abstract

We study the size of the near-critical window for Bernoulli percolation on $\mathbb Z^d$. More precisely, we use a quantitative Grimmett-Marstrand theorem to prove that the correlation length, both below and above criticality, is bounded from above by $\exp(C/|p-p_c|^2)$. Improving on this bound would be a further step towards the conjecture that there is no infinite cluster at criticality on $\mathbb Z^d$ for every $d\ge2$.

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Hugo Duminil-Copin, Gady Kozma, Vincent Tassion. 2019-02-08. Upper bounds on the percolation correlation length. https://arxiv.org/abs/1902.03207

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