{"paper":{"title":"Statistics of a Family of Piecewise Linear Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"J. J. P. Veerman, L. S. Fox, P. J. Oberly","submitted_at":"2020-10-01T00:25:49Z","abstract_excerpt":"We study statistical properties of the truncated flat spot map $f_t(x)$. In particular, we investigate whether for large $n$, the deviations $\\sum_{i=0}^{n-1} \\left(f_t^i(x_0)-\\frac 12\\right)$ upon rescaling satisfy a $Q$-Gaussian distribution if $x_0$ and $t$ are both independently and uniformly distributed on the unit circle. This was motivated by the fact that if $f_t$ is the rotation by $t$, then it has been shown that in this case the rescaled deviations are distributed as a $Q$-Gaussian with $Q=2$ (a Cauchy distribution). This is the only case where a non-trivial (i.e. $Q\\neq 1$) $Q$-Gau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.00155","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.00155/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}