{"paper":{"title":"The hyperbolic geometry of random transpositions","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Nathana\\\"el Berestycki","submitted_at":"2004-10-31T15:59:46Z","abstract_excerpt":"Turn the set of permutations of $n$ objects into a graph $G_n$ by connecting two permutations that differ by one transposition, and let $\\sigma_t$ be the simple random walk on this graph. In a previous paper, Berestycki and Durrett [In Discrete Random Walks (2005) 17--26] showed that the limiting behavior of the distance from the identity at time $cn/2$ has a phase transition at $c=1$. Here we investigate some consequences of this result for the geometry of $G_n$. Our first result can be interpreted as a breakdown for the Gromov hyperbolicity of the graph as seen by the random walk, which occu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411011","kind":"arxiv","version":3},"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"}