{"paper":{"title":"High Minima of Gaussian Processes: Overshoots and Minimizer Locations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.AP","stat.ML"],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Svyatoslav Novikov","submitted_at":"2026-07-22T20:31:36Z","abstract_excerpt":"Let $X(t)$, $t\\in K$, be a centred Gaussian process with continuous sample paths on a compact metric space $K$, and let\n  $M=\\min_{t\\in K}X(t)$. Let $\\sigma_*^2$ denote the minimum covariance energy associated with $X$, and assume that $\\sigma_*^2>0$. Motivated by the results of\n  \\cite{chakrabarty2018asymptotic} for smooth Gaussian processes, we show that, conditionally on $M>u$, the scaled overshoot $u(M-u)$ converges, as $u\\to\\infty$, to an exponential random variable with mean $\\sigma_*^2$. Moreover, every weak subsequential limit of the conditional law of a measurable minimizer of $X$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20714","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.20714/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}