{"paper":{"title":"Records, drift, and the longest increasing subsequence of biased Gaussian random walks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"J. Ricardo G. Mendon\\c{c}a","submitted_at":"2026-05-27T23:48:04Z","abstract_excerpt":"The longest increasing subsequence (LIS) of a random walk has so far been studied mainly for zero-mean, symmetric step increments. We numerically investigate the LIS of biased Gaussian random walks, with unit-variance increments and positive drift $\\mu_{p} = \\Phi^{-1}(p)$, where $p = \\mathbb{P}(\\xi>0)$. In contrast with the symmetric case, we find that for every fixed $p>1/2$ the mean LIS length grows linearly, $\\langle L_{n}(p)\\rangle \\sim a(p)n$, with $a(p)$ increasing from $0$ at $p=1/2$ to $1$ as $p \\to 1$. The record count is also linear, with coefficient $\\lambda(p)$ given by Spitzer's f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29185","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.29185/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}