{"paper":{"title":"A lower bound on the critical parameter of interlacement percolation in high dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Alain-Sol Sznitman","submitted_at":"2010-03-01T13:01:23Z","abstract_excerpt":"We investigate the percolative properties of the vacant set left by random interlacements on Z^d, when d is large. A non-negative parameter u controls the density of random interlacements on Z^d. It is known from arXiv:0704.2560, and arXiv:0808.3344, that there is a non-degenerate critical value u_*, such that the vacant set at level u percolates when u < u_*, and does not percolate when u > u_*. Little is known about u_*, however for large d, random interlacements on Z^d, ought to exhibit similarities to random interlacements on a (2d)-regular tree, for which the corresponding critical parame"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0334","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"}