{"paper":{"title":"Critical dimensions for random walks on random-walk chains","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat","authors_text":"Armin Bunde, H. Eduardo Roman, Savely Rabinovich, Shlomo Havlin","submitted_at":"1996-04-29T09:54:53Z","abstract_excerpt":"The probability distribution of random walks on linear structures generated by random walks in $d$-dimensional space, $P_d(r,t)$, is analytically studied for the case $\\xi\\equiv r/t^{1/4}\\ll1$. It is shown to obey the scaling form $P_d(r,t)=\\rho(r) t^{-1/2} \\xi^{-2} f_d(\\xi)$, where $\\rho(r)\\sim r^{2-d}$ is the density of the chain. Expanding $f_d(\\xi)$ in powers of $\\xi$, we find that there exists an infinite hierarchy of critical dimensions, $d_c=2,6,10,\\ldots$, each one characterized by a logarithmic correction in $f_d(\\xi)$. Namely, for $d=2$, $f_2(\\xi)\\simeq a_2\\xi^2\\ln\\xi+b_2\\xi^2$; for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9604167","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/cond-mat/9604167/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"}