2019/05/20 by Oleg Ivrii, Ivrii, Oleg, Vladimir Marković +1
Computer Science · Mathematics · #30C62 #52C26 #Analytic and geometric function theory #Complex Variables (math.CV) #Computational Geometry and Mesh Generation #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1905.07932
openalex publication_date 2019/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we solve two problems dealing with the homogenization of random media. We show that a random quasiconformal mapping is close to an affine mapping, while a circle packing of a random Delauney triangulation is close to a conformal map, confirming a conjecture of Stephenson. We also show that on a Riemann surface equipped with a conformal metric, a random Delauney triangulation is close to being circle packed.