{"paper":{"title":"Two-Point Correlation Functions and Universality for the Zeros of Systems of SO(n+1)-invariant Gaussian Random Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Pavel M. Bleher, Roland K. W. Roeder, Yushi Homma","submitted_at":"2015-02-05T03:43:55Z","abstract_excerpt":"We study the two-point correlation functions for the zeroes of systems of $SO(n+1)$-invariant Gaussian random polynomials on $\\mathbb{RP}^n$ and systems of ${\\rm isom}(\\mathbb{R}^n)$-invariant Gaussian analytic functions. Our result reflects the same \"repelling,\" \"neutral,\" and \"attracting\" short-distance asymptotic behavior, depending on the dimension, as was discovered in the complex case by Bleher, Shiffman, and Zelditch. For systems of the ${\\rm isom}(\\mathbb{R}^n)$-invariant Gaussian analytic functions we also obtain a fast decay of correlations at long distances.\n  We then prove that the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01427","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"}