{"paper":{"title":"Percolation of random nodal lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Damien Gayet (IF), Vincent Beffara (IF)","submitted_at":"2016-05-27T12:22:37Z","abstract_excerpt":"We prove  a Russo-Seymour-Welsch percolation theorem  for nodal domains and nodal lines  associated to a natural  infinite dimensional space of  real analytic functions on  the real plane. More precisely, let  $U$  be  a   smooth  connected  bounded  open  set   in  $\\mathbb R^2$  and  $\\gamma,  \\gamma'$  two disjoint  arcs  of  positive length  in  the  boundary of $U$. We prove that there exists a positive constant  $c$, such that for any  positive scale $s$, with probability at  least    $c$    there    exists    a    connected    component    of  $\\{x\\in  \\bar U,  \\, f(sx)  \\textgreater{} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08605","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"}