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arXiv · 2509.10990

On the Continuity of Enhancement Percolation

Paul Duncan·Benjamin Schweinhart·David Sivakoff
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Abstract

We study bond percolation in $\mathbb{Z}^d$ with an unbounded family of enhancements that enable additional bonds to act as open. A natural question is whether percolation occurs in this model if and only if percolation also occurs in the system with a finite subcollection of enhancements. We give an affirmative answer in dimension $d=2$ for symmetric families of connected enhancements, and in dimensions $d\ge 3$ we prove a partial result.

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Paul Duncan, Benjamin Schweinhart, David Sivakoff. 2025-09-13. On the Continuity of Enhancement Percolation. https://arxiv.org/abs/2509.10990

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