{"paper":{"title":"Large deviations for zeros of $P(\\phi)_2$ random polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Renjie Feng, Steve Zelditch","submitted_at":"2010-09-27T02:26:42Z","abstract_excerpt":"We extend results of Zeitouni-Zelditch on large deviations principles for zeros of Gaussian random polynomials $s$ in one complex variable to certain non-Gaussian ensembles that we call $P(\\phi)_2$ random polynomials. The probability measures are of the form $e^{- S(f)} df$ where the actions $S(f)$ are finite dimensional analgoues of those of $P(\\phi)_2$ quantum field theory. The speed and rate function are the same as in the associated Gaussian case. As a corollary, we prove that the expected distribution of zeros in the $P(\\phi)_2$ ensembles tends to the same equilibrium measure as in the Ga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5142","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":""},"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"}