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Expansion for the critical point of site percolation: the first three terms

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arxiv 1912.04584 v2 pith:HB62EOK7 submitted 2019-12-10 math.PR

Markus Heydenreich , Kilian Matzke This is my paper · ORCID
classification math.PR
keywords termscriticalexpansionfirstpercolationpointsitethree
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abstract

We expand the critical point for site percolation on the $d$-dimensional hypercubic lattice in terms of inverse powers of $2d$, and we obtain the first three terms rigorously. This is achieved using the lace expansion.

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  1. Lace Expansion and Mean-Field Behavior for the Random Connection Model

    math.PR 2019-08 conditional novelty 8.0 of 10

    The random connection model in high dimensions satisfies the triangle condition and the critical exponent gamma = 1, proven via a new continuum lace expansion.

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