{"paper":{"title":"L\\'{e}vy-like flights and fractal geometry of finite point sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","nlin.AO","physics.comp-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"A. S. Kapoyannis, F. K. Diakonos, Konstantinos Chalas","submitted_at":"2026-05-14T14:07:09Z","abstract_excerpt":"We study L\\'{e}vy-like and truncated L\\'{e}vy-like flights with step probability distribution of the form $r^{-1+\\nu}$ for negative, positive, and zero $\\nu$, focusing on the appearance of fractal geometry characteristics in the generated point sets. Forming ensembles of such point sets with fixed multiplicity, we develop simulation techniques leading to the desired value of correlation dimension in a vast continuous interval of scales. In particular, we demonstrate the possibility to produce ensembles of data sets with a low number of points with the needed properties. Furthermore, we show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.14861","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"}