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A Pivotal Amplitude for Voronoi Percolation from Cardy's Formula

Source: github.com/openai/math/tree/main/preprints/A-Pivotal-Amplit…

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OpenAI Mathopenai-math/A-Pivotal-Amplitude-for-Voronoi-Percolation-from-Cardys-FormulaOct 5, 2026math.PRAI-generatedscore 0

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.

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