{"paper":{"title":"Damped random walks and the characteristic polynomial of the weighted Laplacian on a graph","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Hariharan Narayanan, Madhav Desai","submitted_at":"2005-06-22T18:53:57Z","abstract_excerpt":"For $\\lambda>0$, we define a $\\lambda$-damped random walk to be a random walk that is started from a random vertex of a graph and stopped at each step with probability $\\frac{\\lambda}{1+\\lambda}$, otherwise continued with probability $\\frac{1}{1+\\lambda}$. We use the Aldous-Broder algorithm (\\cite{aldous, broder}) of generating a random spanning tree and the Matrix-tree theorem to relate the values of the characteristic polynomial of the Laplacian at $\\pm \\lambda$ and the stationary measures of the sets of nodes visited by $i$ independent $\\lambda$-damped random walks for $i \\in \\N$. As a coro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506460","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"}