{"paper":{"title":"Spectrum of large random reversible Markov chains: Heavy-tailed weights on the complete graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.PR","authors_text":"Charles Bordenave, Djalil Chafa\\\"i, Pietro Caputo","submitted_at":"2009-03-20T14:26:00Z","abstract_excerpt":"We consider the random reversible Markov kernel K obtained by assigning i.i.d. nonnegative weights to the edges of the complete graph over n vertices and normalizing by the corresponding row sum. The weights are assumed to be in the domain of attraction of an $\\alpha$-stable law, $\\alpha\\in(0,2)$. When $1\\leq\\alpha<2$, we show that for a suitable regularly varying sequence $\\kappa_n$ of index $1-1/\\alpha$, the limiting spectral distribution $\\mu_{\\alpha}$ of $\\kappa_nK$ coincides with the one of the random symmetric matrix of the un-normalized weights (L\\'{e}vy matrix with i.i.d. entries). In "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3528","kind":"arxiv","version":5},"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"}