{"paper":{"title":"Root Dynamics of Differentiated Polynomials with Rotationally Invariant Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS"],"primary_cat":"math.PR","authors_text":"Joseph Najnudel, Truong Vu","submitted_at":"2026-07-06T13:28:38Z","abstract_excerpt":"The dynamics of polynomial roots under repeated differentiation has recently been conjectured to converge to a limiting measure governed by specific nonlinear PDEs, the conjectures being shown in some particular settings. For rotationally invariant initial distributions, a deterministic structured sampling model placing roots on concentric circles was recently introduced by Galligo, Najnudel, and Vu. In this paper, the authors proved convergence under the technical growth condition $m_n / (n \\log n) \\to \\infty$, where $n$ is the number of circles and $m_n$ is the number of points per circle. I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05054","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/2607.05054/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"}