{"paper":{"title":"Ordering statistics of 4 random walkers on the line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Brian Helenbrook, Daniel ben-Avraham","submitted_at":"2018-01-10T16:59:16Z","abstract_excerpt":"We study the ordering statistics of 4 random walkers on the line, obtaining a much improved estimate for the long-time decay exponent of the probability that a particle leads to time $t$; $P_{\\rm lead}(t)\\sim t^{-0.91287850}$, and that a particle lags to time $t$ (never assumes the lead); $P_{\\rm lag}(t)\\sim t^{-0.30763604}$. Exponents of several other ordering statistics for $N=4$ walkers are obtained to 8 digits accuracy as well. The subtle correlations between $n$ walkers that lag {\\em jointly}, out of a field of $N$, are discussed: For $N=3$ there are no correlations and $P_{\\rm lead}(t)\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03453","kind":"arxiv","version":1},"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"}