{"paper":{"title":"Possible Connection between the Optimal Path and Flow in Percolation Clusters","license":"","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Eduardo L\\'opez, H. Eugene Stanley, Lidia A. Braunstein, Sergey V. Buldyrev, Shlomo Havlin","submitted_at":"2005-10-06T01:49:40Z","abstract_excerpt":"We study the behavior of the optimal path between two sites separated by a distance $r$ on a $d$-dimensional lattice of linear size $L$ with weight assigned to each site. We focus on the strong disorder limit, i.e., when the weight of a single site dominates the sum of the weights along each path. We calculate the probability distribution $P(\\ell_{\\rm opt}|r,L)$ of the optimal path length $\\ell_{\\rm opt}$, and find for $r\\ll L$ a power law decay with $\\ell_{\\rm opt}$, characterized by exponent $g_{\\rm opt}$. We determine the scaling form of $P(\\ell_{\\rm opt}|r,L)$ in two- and three-dimensional"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0510127","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":""},"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"}