{"paper":{"title":"Trace reconstruction with varying deletion probabilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Lisa Hartung, Nina Holden, Yuval Peres","submitted_at":"2017-08-07T17:35:40Z","abstract_excerpt":"In the trace reconstruction problem an unknown string ${\\bf x}=(x_0,\\dots,x_{n-1})\\in\\{0,1,...,m-1\\}^n$ is observed through the deletion channel, which deletes each $x_k$ with a certain probability, yielding a contracted string $\\widetilde{\\bf X}$. Earlier works have proved that if each $x_k$ is deleted with the same probability $q\\in[0,1)$, then $\\exp(O(n^{1/3}))$ independent copies of the contracted string $\\widetilde{\\bf X}$ suffice to reconstruct $\\bf x$ with high probability. We extend this upper bound to the setting where the deletion probabilities vary, assuming certain regularity condi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02216","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"}