{"paper":{"title":"Subdiffusive concentration in first-passage percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jack Hanson, Michael Damron, Philippe Sosoe","submitted_at":"2014-01-05T17:52:05Z","abstract_excerpt":"We prove exponential concentration in i.i.d. first-passage percolation in $Z^d$ for all $d \\geq 2$ and general edge-weights $(t_e)$. Precisely, under an exponential moment assumption $E e^{\\alpha t_e}< \\infty$ for some $\\alpha>0$) on the edge-weight distribution, we prove the inequality $$ P(|T(0,x)-E T(0,x)| \\geq \\lambda \\sqrt{\\frac{|x|}{log |x|}}) \\leq ce^{-c' \\lambda}, |x|>1 $$ for the point-to-point passage time $T(0,x)$. Under a weaker assumption $E t_e^2(\\log t_e)_+< \\infty$ we show a corresponding inequality for the lower-tail of the distribution of $T(0,x)$. These results extend work o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0917","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"}