{"paper":{"title":"On the conditional distributions and the efficient simulations of exponential integrals of Gaussian random fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gongjun Xu, Jingchen Liu","submitted_at":"2012-04-25T02:45:00Z","abstract_excerpt":"In this paper, we consider the extreme behavior of a Gaussian random field $f(t)$ living on a compact set $T$. In particular, we are interested in tail events associated with the integral $\\int_Te^{f(t)}\\,dt$. We construct a (non-Gaussian) random field whose distribution can be explicitly stated. This field approximates the conditional Gaussian random field $f$ (given that $\\int_Te^{f(t)}\\,dt$ exceeds a large value) in total variation. Based on this approximation, we show that the tail event of $\\int_Te^{f(t)}\\,dt$ is asymptotically equivalent to the tail event of $\\sup_T\\gamma(t)$ where $\\gam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5546","kind":"arxiv","version":3},"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"}