{"paper":{"title":"Convolutions of Cantor measures without resonance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Fedor Nazarov, Pablo Shmerkin, Yuval Peres","submitted_at":"2009-05-23T20:59:11Z","abstract_excerpt":"Denote by $\\mu_a$ the distribution of the random sum $(1-a) \\sum_{j=0}^\\infty \\omega_j a^j$, where $P(\\omega_j=0)=P(\\omega_j=1)=1/2$ and all the choices are independent. For $0<a<1/2$, the measure $\\mu_a$ is supported on $C_a$, the central Cantor set obtained by starting with the closed united interval, removing an open central interval of length $(1-2a)$, and iterating this process inductively on each of the remaining intervals.\n  We investigate the convolutions $\\mu_a * (\\mu_b \\circ S_\\lambda^{-1})$, where $S_\\lambda(x)=\\lambda x$ is a rescaling map. We prove that if the ratio $\\log b/\\log a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3850","kind":"arxiv","version":1},"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"}