{"paper":{"title":"Optimal flow through the disordered lattice","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Aldous","submitted_at":"2005-11-29T00:16:44Z","abstract_excerpt":"Consider routing traffic on the N x N torus, simultaneously between all source-destination pairs, to minimize the cost $\\sum_ec(e)f^2(e)$, where f(e) is the volume of flow across edge e and the c(e) form an i.i.d. random environment. We prove existence of a rescaled $N\\to \\infty$ limit constant for minimum cost, by comparison with an appropriate analogous problem about minimum-cost flows across a M x M subsquare of the lattice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511694","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"}