{"paper":{"title":"Time Correlation Exponents in Last Passage Percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Riddhipratim Basu, Shirshendu Ganguly","submitted_at":"2018-07-24T17:56:36Z","abstract_excerpt":"For directed last passage percolation on $\\mathbb{Z}^2$ with exponential passage times on the vertices, let $T_{n}$ denote the last passage time from $(0,0)$ to $(n,n)$. We consider asymptotic two point correlation functions of the sequence $T_{n}$. In particular we consider ${\\rm Corr}(T_{n}, T_{r})$ for $r\\le n$ where $r,n\\to \\infty$ with $r\\ll n$ or $n-r \\ll n$. We show that in the former case ${\\rm Corr}(T_{n}, T_{r})=\\Theta((\\frac{r}{n})^{1/3})$ whereas in the latter case $1-{\\rm Corr}(T_{n}, T_{r})=\\Theta ((\\frac{n-r}{n})^{2/3})$. The argument revolves around finer understanding of polym"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09260","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"}