{"paper":{"title":"Asymptotics for Lipschitz percolation above tilted planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Drewitz, Maite Wilke-Berenguer, Michael Scheutzow","submitted_at":"2015-04-21T12:35:20Z","abstract_excerpt":"We consider Lipschitz percolation in $d+1$ dimensions above planes tilted by an angle $\\gamma$ along one or several coordinate axes. In particular, we are interested in the asymptotics of the critical probability as $d \\to \\infty$ as well as $\\gamma \\to \\pi/4.$ Our principal results show that the convergence of the critical probability to 1 is polynomial as $d\\to \\infty$ and $\\gamma \\to \\pi/4.$ In addition, we identify the correct order of this polynomial convergence and in $d=1$ we also obtain the correct prefactor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05405","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"}