{"paper":{"title":"Large-n conditional facedness m_n of 3D Poisson-Voronoi cells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"H.J. Hilhorst","submitted_at":"2014-01-10T15:07:11Z","abstract_excerpt":"We consider the three-dimensional Poisson-Voronoi tessellation and study the average facedness m_n of a cell known to neighbor an n-faced cell. Whereas Aboav's law states that m_n=A+B/n, theoretical arguments indicate an asymptotic expansion m_n = 8 + k_1 n^{-1/6} +.... Recent new Monte Carlo data due to Lazar et al., based on a very large data set, now clearly rule out Aboav's law. In this work we determine the numerical value of k_1 and compare the expansion to the Monte Carlo data. The calculation of k_1 involves an auxiliary planar cellular structure composed of circular arcs, that we will"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2363","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}