{"paper":{"title":"Real zeros of random analytic functions associated with geometries of constant curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hendrik Flasche, Zakhar Kabluchko","submitted_at":"2018-02-07T11:34:49Z","abstract_excerpt":"Let $\\xi_0, \\xi_1, \\dots$ be i.i.d. random variables with zero mean and unit variance. We study the following four families of random analytic functions: $\\sum_{k=0}^n \\sqrt{\\binom nk} \\xi_k z^k$ (spherical polynomials), $\\sum_{k=0}^\\infty \\sqrt{\\frac{n^k}{k!}} \\xi_k z^k$ (flat random analytic function), $\\sum_{k=0}^\\infty \\sqrt{\\binom {n+k-1} k} \\xi_k z^k$ (hyperbolic random analytic functions), $\\sum_{k=0}^n \\sqrt{\\frac{n^k}{k!}} \\xi_k z^k$ (Weyl polynomials). We compute explicitly the limiting mean density of real zeroes of these random functions. More precisely, we provide a formula for $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02390","kind":"arxiv","version":3},"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"}