{"paper":{"title":"On random surface area","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.PR","authors_text":"Dmitry Zaporozhets, Ildar Ibragimov","submitted_at":"2011-02-17T07:10:17Z","abstract_excerpt":"Consider a random smooth Gaussian field $G(x):F\\to\\mathbb{R}$, where $F$ is a compact in $\\mathbb{R}^d$. We derive a formula for average area of a surface generated by the equation $G(x)=0$ and give some applications. As an auxiliary result we obtain an integral expression for area of a surface induced by zeros of a \\emph{non-random} smooth field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3509","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"}