{"paper":{"title":"Probabilistic Condition Number Estimates For Real Polynomial Systems I: A Broader Family Of Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NA"],"primary_cat":"math.PR","authors_text":"Alperen A. Erg\\\"ur, Grigoris Paouris, J. Maurice Rojas","submitted_at":"2016-11-04T02:19:05Z","abstract_excerpt":"We consider the sensitivity of real roots of polynomial systems with respect to perturbations of the coefficients. In particular - for a version of the condition number defined by Cucker, Krick, Malajovich, and Wschebor - we establish new probabilistic estimates that allow a much broader family of measures than considered earlier. We also generalize further by allowing over-determined systems. Along the way, we derive new Lipshitz estimates for polynomial maps from R^n to R^m, extending earlier work of Kellog on the case m=1, which may be of independent interest. In Part II, we study smoothed "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01246","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"}