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arXiv · 2103.17013

The critical two-point function for long-range percolation on the hierarchical lattice

Tom Hutchcroft
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Abstract

We prove up-to-constants bounds on the two-point function (i.e., point-to-point connection probabilities) for critical long-range percolation on the $d$-dimensional hierarchical lattice. More precisely, we prove that if we connect each pair of points $x$ and $y$ by an edge with probability $1-\exp(-\beta\|x-y\|^{-d-\alpha})$, where $0<\alpha d/3$.

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Tom Hutchcroft. 2021-03-31. The critical two-point function for long-range percolation on the hierarchical lattice. https://arxiv.org/abs/2103.17013

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