{"paper":{"title":"Perturbing the hexagonal circle packing: a percolation perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MG","math.MP"],"primary_cat":"math.PR","authors_text":"Alexandre Stauffer, Itai Benjamini","submitted_at":"2011-04-05T08:17:35Z","abstract_excerpt":"We consider the hexagonal circle packing with radius 1/2 and perturb it by letting the circles move as independent Brownian motions for time t. It is shown that, for large enough t, if \\Pi_t is the point process given by the center of the circles at time t, then, as t\\to\\infty, the critical radius for circles centered at \\Pi_t to contain an infinite component converges to that of continuum percolation (which was shown---based on a Monte Carlo estimate---by Balister, Bollob\\'as and Walters to be strictly bigger than 1/2). On the other hand, for small enough t, we show (using a Monte Carlo estim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0762","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"}