{"paper":{"title":"On hitting times for simple random walk on dense Erd\\\"os-R\\'enyi random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Felipe Torres, Matthias L\\\"owe","submitted_at":"2013-10-07T14:18:01Z","abstract_excerpt":"Let $G(N,p)=(V,E)$ be an Erd\\\"os-R\\'enyi random graph and $(X_n)_{n \\in \\mathbb{N}}$ be a simple random walk on it. We study the the order of magnitude of $\\sum_{i \\in V} \\pi_ih_{ij} $ where $\\pi_i=d_i / 2|E|$ for $d_i$ the number of neighbors of node $i$ and $h_{ij}$ the hitting time for $(X_n)_{n \\in \\mathbb{N}}$ between nodes $i$ and $j$, in a regime of $p=p(N)$ such that $G(N,p)$ is almost surely connected as $N\\to\\infty$. Our main result is that $\\sum_{i \\in V} \\pi_ih_{ij} $ is almost surely of order $N(1+o(1))$ as $N\\to \\infty$, which coincides with previous results in the physics litera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1792","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"}