{"paper":{"title":"Dynamics of zeroes under repeated differentiation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.CA","math.MP"],"primary_cat":"math.PR","authors_text":"Jeremy Hoskins, Zakhar Kabluchko","submitted_at":"2020-10-27T14:30:24Z","abstract_excerpt":"Consider a random polynomial $P_n$ of degree $n$ whose roots are independent random variables sampled according to some probability distribution $\\mu_0$ on the complex plane $\\mathbb C$. It is natural to conjecture that, for a fixed $t\\in [0,1)$ and as $n\\to\\infty$, the zeroes of the $[tn]$-th derivative of $P_n$ are distributed according to some measure $\\mu_t$ on $\\mathbb C$. Assuming either that $\\mu_0$ is concentrated on the real line or that it is rotationally invariant, Steinerberger [Proc. AMS, 2019] and O'Rourke and Steinerberger [arXiv:1910.12161] derived nonlocal transport equations "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.14320","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.14320/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"}