{"paper":{"title":"A combinatorial result with applications to self-interacting random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mark Holmes, Thomas S. Salisbury","submitted_at":"2011-05-25T21:39:11Z","abstract_excerpt":"We give a series of combinatorial results that can be obtained from any two collections (both indexed by $\\Z\\times \\N$) of left and right pointing arrows that satisfy some natural relationship. When applied to certain self-interacting random walk couplings, these allow us to reprove some known transience and recurrence results for some simple models. We also obtain new results for one-dimensional multi-excited random walks and for random walks in random environments in all dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5157","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"}