{"paper":{"title":"Multi-point correlations for two dimensional coalescing random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"math.PR","authors_text":"Jamie Lukins, Oleg Zaboronski, Roger Tribe","submitted_at":"2017-07-19T18:07:28Z","abstract_excerpt":"This paper considers an infinite system of instantaneously coalescing rate one simple random walks on $\\mathbb{Z}^2$, started from the initial condition with all sites in $\\mathbb{Z}^2$ occupied. We show that the correlation functions of the model decay, for any $N \\geq 2$, as \\[ \\rho_N (x_1,\\ldots,x_N;t) = \\frac{c_0(x_1,\\ldots,x_N)}{\\pi^N} (\\log t)^{N-{N \\choose 2}} t^{-N} \\left(1 + O\\left( \\frac{1}{\\log^{\\frac12-\\delta}\\!t} \\right) \\right) \\] as $t \\to\\infty$. This generalises the results for $N=1$ due to Bramson and Griffeath and confirms a prediction in the physics literature for $N>1$. An"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06250","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"}