{"paper":{"title":"Central Limit Theorem for probability measures defined by sum-of-digits function in base 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.PR","authors_text":"I2M), Jordan Emme (1), Pascal Hubert (1) ((1) AMU","submitted_at":"2016-05-20T11:31:29Z","abstract_excerpt":"In this paper we prove a central limit theorem for some probability measures defined as asymtotic densities of integer sets defined via sum-of-digit-function. To any integer a we can associate a measure on Z called $\\mu$a such that, for any d, $\\mu$a(d) is the asymptotic density of the set of integers n such that s\\_2(n + a) -- s\\_2(n) = d where s\\_2(n) is the number of digits \"1\" in the binary expansion of n. We express this probability measure as a product of matrices. Then we take a sequence of integers (a\\_X(n)) n$\\in$N via a balanced Bernoulli process. We prove that, for almost every sequ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06297","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"}