{"paper":{"title":"Large Deviations for Brownian Intersection Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chiranjib Mukherjee, Wolfgang Koenig","submitted_at":"2011-05-05T13:14:37Z","abstract_excerpt":"We consider $p$ independent Brownian motions in $\\R^d$. We assume that $p\\geq 2$ and $p(d-2)<d$. Let $\\ell_t$ denote the intersection measure of the $p$ paths by time $t$, i.e., the random measure on $\\R^d$ that assigns to any measurable set $A\\subset \\R^d$ the amount of intersection local time of the motions spent in $A$ by time $t$. Earlier results of Chen \\cite{Ch09} derived the logarithmic asymptotics of the upper tails of the total mass $\\ell_t(\\R^d)$ as $t\\to\\infty$. In this paper, we derive a large-deviation principle for the normalised intersection measure $t^{-p}\\ell_t$ on the set of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1063","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"}