{"paper":{"title":"Multifractal structure of Bernoulli convolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Boris Solomyak, Pablo Shmerkin, Thomas Jordan","submitted_at":"2010-11-08T22:47:36Z","abstract_excerpt":"Let $\\nu_\\lambda^p$ be the distribution of the random series $\\sum_{n=1}^\\infty i_n \\lambda^n$, where $i_n$ is a sequence of i.i.d. random variables taking the values 0,1 with probabilities $p,1-p$. These measures are the well-known (biased) Bernoulli convolutions.\n  In this paper we study the multifractal spectrum of $\\nu_\\lambda^p$ for typical $\\lambda$. Namely, we investigate the size of the sets\n  \\[ \\Delta_{\\lambda,p}(\\alpha) = \\left\\{x\\in\\R: \\lim_{r\\searrow 0} \\frac{\\log \\nu_\\lambda^p(B(x,r))}{\\log r} =\\alpha\\right\\}. \\]\n  Our main results highlight the fact that for almost all, and in s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1938","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"}