{"paper":{"title":"Dimensional Crossover in Anisotropic Percolation on $Z^{d+s}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"R\\'emy Sanchis, Roger W. C. Silva","submitted_at":"2017-06-22T21:19:53Z","abstract_excerpt":"We consider bond percolation on $\\Z^d\\times \\Z^s$ where edges of $\\Z^d$ are open with probability $p<p_c(\\Z^d)$ and edges of $\\Z^s$ are open with probability $q$, independently of all others. We obtain bounds for the critical curve in $(p, q)$, with $p$ close to the critical threshold $p_c(\\Z^d)$. The results are related to the so-called dimensional crossover from $\\Z^d$ to $\\Z^{d+s}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07495","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"}