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Random walk on sphere packings and Delaunay triangulations in arbitrary dimension

Ahmed Bou-Rabee

Palomar Registrypalomar/PALOMAR-2026-10-27-000015Oct 27, 2026math.PRscore 0

A Lean 4 formalization of the paper "Random walk on sphere packings and Delaunay triangulations in arbitrary dimension" by Bou-Rabee and Gwynne: on orthogonal tilings with small mesh and one of three regularity hypotheses, the stopped conductance-weighted random walk converges to stopped Brownian motion modulo time parametrization (Theorem A) and the discrete Dirichlet problem converges (Theorem B, both alternatives); Poisson-Voronoi tessellations satisfy the hypotheses (Proposition 1.1); and simple random walk on a bounded-degree sphere packing need not converge (Theorem 6.1); for any…

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