{"id":"openai-math/A-Pivotal-Amplitude-for-Voronoi-Percolation-from-Cardys-Formula","pdf":"https://github.com/openai/math/blob/main/preprints/A-Pivotal-Amplitude-for-Voronoi-Percolation-from-Cardys-Formula-October-5-2026/voronoi-pivotal-amplitude.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Pivotal-Amplitude-for-Voronoi-Percolation-from-Cardys-Formula-October-5-2026","tags":["percolation","probability","statistical-mechanics"],"score":0,"title":"A Pivotal Amplitude for Voronoi Percolation from Cardy's Formula","domain":"Probability and statistical mechanics","family":"224","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"Taking Cardy's conformal crossing formula for critical planar Poisson–Voronoi percolation in every bounded Jordan quadrilateral as an input, we prove that the expected number of color-pivotal cells for a unit-square crossing is asymptotic to a positive constant times $`\\varepsilon ^{-3/4}`$, where the point intensity is $`\\varepsilon ^{-2}`$. No rate of convergence in Cardy's formula is required.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Critical and quenched near-critical universality for Poisson–Voronoi percolation"}