{"paper":{"title":"Continuum percolation in high dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Baptiste Gou\\'er\\'e (MAPMO), Regine Marchand (IECL)","submitted_at":"2011-08-31T06:44:54Z","abstract_excerpt":"Consider a Boolean model $\\Sigma$ in $\\R^d$. The centers are given by a homogeneous Poisson point process with intensity $\\lambda$ and the radii of distinct balls are i.i.d.\\ with common distribution $\\nu$. The critical covered volume is the proportion of space covered by $\\Sigma$ when the intensity $\\lambda$ is critical for percolation. Previous numerical simulations and heuristic arguments suggest that the critical covered volume may be minimal when $\\nu$ is a Dirac measure. In this paper, we prove that it is not the case at least in high dimension. To establish this result we study the asym"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6133","kind":"arxiv","version":2},"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"}