Voronoi Percolation: Topological Stability and Giant Cycles

Benjamin Schweinhart; Morgan Shuman

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arXiv · 2601.00793

Voronoi Percolation: Topological Stability and Giant Cycles

Benjamin Schweinhart·Morgan Shuman

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Abstract

We study the topological stability of Voronoi percolation in higher dimensions. We show that slightly increasing p allows a discretization that preserves increasing topological properties with high probability. This strengthens a theorem of Bollob\'as and Riordan and generalizes it to higher dimensions. As a consequence, we prove a sharp phase transition for the emergence of i-dimensional giant cycles in Voronoi percolation on the 2i-dimensional torus.

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Benjamin Schweinhart, Morgan Shuman. 2026-01-02. Voronoi Percolation: Topological Stability and Giant Cycles. https://arxiv.org/abs/2601.00793

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