{"paper":{"title":"Finite free perpetuities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Bartosz Ko{\\l}odziejek, Julia Le Bihan","submitted_at":"2026-06-17T14:28:50Z","abstract_excerpt":"We introduce and study finite free perpetuities, defined as monic polynomial solutions of degree $n$ to the affine fixed-point equation \\[ p(z) = \\mathbb{E}\\!\\left[ A^{n}\\,p\\!\\left(\\frac{z-B}{A}\\right)\\mathbf{1}_{\\{A\\neq0\\}} \\right] + \\mathbb{E}\\!\\left[ (z-B)^n\\mathbf{1}_{\\{A=0\\}} \\right], \\] where $A$ and $B$ are complex-valued random variables with finite moments up to order $n$. Equivalently, if $p(z)=\\mathbb{E}[(z-X)^n]$, then $p$ encodes a truncated moment version of the classical perpetuity equation $X\\stackrel{d}{=}AX+B$ with $X$ and $(A,B)$ independent. This places finite free perpetui"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19115","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.19115/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"}