{"paper":{"title":"A Counterexample to Monotonicity of Relative Mass in Random Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Igor Shinkar, Oded Regev","submitted_at":"2015-06-29T14:03:25Z","abstract_excerpt":"For a finite undirected graph $G = (V,E)$, let $p_{u,v}(t)$ denote the probability that a continuous-time random walk starting at vertex $u$ is in $v$ at time $t$. In this note we give an example of a Cayley graph $G$ and two vertices $u,v \\in G$ for which the function \\[ r_{u,v}(t) = \\frac{p_{u,v}(t)}{p_{u,u}(t)} \\qquad t \\geq 0 \\] is not monotonically non-decreasing. This answers a question asked by Peres in 2013."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08631","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"}