{"paper":{"title":"Random walk with barycentric self-interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrew R. Wade, Francis Comets, Mikhail V. Menshikov, Stanislav Volkov","submitted_at":"2010-03-16T10:34:09Z","abstract_excerpt":"We study the asymptotic behaviour of a $d$-dimensional self-interacting random walk $X_n$ ($n = 1,2,...$) which is repelled or attracted by the centre of mass $G_n = n^{-1} \\sum_{i=1}^n X_i$ of its previous trajectory. The walk's trajectory $(X_1,...,X_n)$ models a random polymer chain in either poor or good solvent. In addition to some natural regularity conditions, we assume that the walk has one-step mean drift directed either towards or away from its current centre of mass $G_n$ and of magnitude $\\| X_n - G_n \\|^{-\\beta}$ for $\\beta \\geq 0$. When $\\beta <1$ and the radial drift is outwards"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3121","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"}