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arXiv (math.PR)
2026-06-12
Voronoi Percolation: Topological Stability and Giant Cycles
作者:
arXiv:2601.00793v2 Announce Type: replace 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 Bollobás 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.