{"paper":{"title":"Unimodality for free L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Noriyoshi Sakuma, Takahiro Hasebe","submitted_at":"2015-08-06T05:03:50Z","abstract_excerpt":"We will prove that: (1) A symmetric free L\\'evy process is unimodal if and only if its free L\\'evy measure is unimodal; (2) Every free L\\'evy process with boundedly supported L\\'evy measure is unimodal in sufficiently large time. (2) is completely different property from classical L\\'evy processes. On the other hand, we find a free L\\'evy process such that its marginal distribution is not unimodal for any time $s>0$ and its free L\\'evy measure does not have a bounded support. Therefore, we conclude that the boundedness of the support of free L\\'evy measure in (2) cannot be dropped. For the pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01285","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"}