{"paper":{"title":"Diffuse Behaviour of Ergodic Sums Over Rotations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Jean-Pierre Conze (IRMAR), Stefano Isola, St\\'ephane Le Borgne (IRMAR)","submitted_at":"2017-05-30T11:26:28Z","abstract_excerpt":"For a rotation by an irrational $\\alpha$ on the circle and a BV function $\\varphi$, we  study the variance of the ergodic sums $S_L \\varphi(x) := \\sum_{j=0}^{L -1} \\, \\varphi(x + j\\alpha)$. When $\\alpha$ is not of constant type, we construct sequences $(L_N)$ such that, at some scale, the ergodic sums $S_{L_N} \\varphi$  satisfy an ASIP. Explicit non-degenerate examples are given, with an application to the rectangular periodic billiard in the plane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10550","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"}