{"paper":{"title":"Stationary distribution and cover time of random walks on random digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Alan Frieze, Colin Cooper","submitted_at":"2011-03-22T17:24:54Z","abstract_excerpt":"We study properties of a simple random walk on the random digraph D_{n,p} when np={d\\log n},\\; d>1.\n  We prove that whp the stationary probability pi_v of a vertex v is asymptotic to deg^-(v)/m where deg^-(v) is the in-degree of v and m=n(n-1)p is the expected number of edges of D_{n,p}. If d=d(n) tends to infinity with n, the stationary distribution is asymptotically uniform whp.\n  Using this result we prove that, for d>1, whp the cover time of D_{n,p} is asymptotic to d\\log (d/(d-1))n\\log n. If d=d(n) tends to infinity with n, then the cover time is asymptotic to n\\log n."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4317","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"}