{"paper":{"title":"On the probability that a stationary Gaussian process with spectral gap remains non-negative on a long interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.PR","authors_text":"Benjamin Jaye, Fedor Nazarov, Naomi Feldheim, Ohad Feldheim, Shahaf Nitzan","submitted_at":"2018-01-31T10:43:44Z","abstract_excerpt":"Let $f$ be a zero-mean continuous stationary Gaussian process on ${\\mathbb R}$ whose spectral measure vanishes in a $\\delta$-neighborhood of the origin. Then the probability that $f$ stays non-negative on an interval of length $L$ is at most $e^{-c\\delta^2 L^2}$ with some absolute $c>0$ and the result is sharp without additional assumptions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10392","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"}