{"paper":{"title":"Winding angles of long lattice walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"cond-mat.stat-mech","authors_text":"Yacov Kantor, Yosi Hammer","submitted_at":"2016-06-09T10:57:42Z","abstract_excerpt":"We study the winding angles of random and self-avoiding walks on square and cubic lattices with number of steps $N$ ranging up to $10^7$. We show that the mean square winding angle $\\langle\\theta^2\\rangle$ of random walks converges to the theoretical form when $N\\rightarrow\\infty$. For self-avoiding walks on the square lattice, we show that the ratio $\\langle\\theta^4\\rangle/\\langle\\theta^2\\rangle^2$ converges slowly to the Gaussian value 3. For self avoiding walks on the cubic lattice we find that the ratio $\\langle\\theta^4\\rangle/\\langle\\theta^2\\rangle^2$ exhibits non-monotonic dependence on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02907","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"}