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arXiv · 1911.04159

Critical site percolation in high dimension

Markus Heydenreich·Kilian Matzke
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Abstract

We use the lace expansion to prove an infra-red bound for site percolation on the hypercubic lattice in high dimension. This implies the triangle condition and allows us to derive several critical exponents that characterize mean-field behavior in high dimensions.

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Markus Heydenreich, Kilian Matzke. 2019-11-11. Critical site percolation in high dimension. https://doi.org/10.1007/s10955-020-02607-y

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