{"paper":{"title":"Shortest paths on systems with power-law distributed long-range connections","license":"","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Cristian F. Moukarzel, Marcio Argollo de Menezes","submitted_at":"2002-01-07T21:36:07Z","abstract_excerpt":"We discuss shortest-path lengths $\\ell(r)$ on periodic rings of size L supplemented with an average of pL randomly located long-range links whose lengths are distributed according to $P_l \\sim l^{-\\xpn}$. Using rescaling arguments and numerical simulation on systems of up to $10^7$ sites, we show that a characteristic length $\\xi$ exists such that $\\ell(r) \\sim r$ for $r<\\xi$ but $\\ell(r) \\sim r^{\\theta_s(\\xpn)}$ for $r>>\\xi$. For small p we find that the shortest-path length satisfies the scaling relation $\\ell(r,\\xpn,p)/\\xi = f(\\xpn,r/\\xi)$. Three regions with different asymptotic behaviors "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0201083","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"}