{"paper":{"title":"Overcrowding for zeros of Hyperbolic Gaussian analytic functions","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CV","authors_text":"Keren Mor Waknin","submitted_at":"2022-09-13T10:02:56Z","abstract_excerpt":"We consider the family $\\{f_L\\}_{L>0}$ of Gaussian analytic functions in the unit disk, distinguished by the invariance of their zero set with respect to hyperbolic isometries. Let $n_L\\left(r\\right)$ be the number of zeros of $f_L$ in a disk of radius $r$. We study the asymptotic probability of the rare event where there is an overcrowding of the zeros as $r\\uparrow1$, i.e. for every $L>0$, we are looking for the asymptotics of the probability $\\mathbb{P}\\left[n_L(r)\\geq V(r)\\right]$ with $V\\left(r\\right)$ large compared to the $\\mathbb{E}\\left[n_L\\left(r\\right)\\right]$. Peres and Vir\\'ag sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.05854","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.05854/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"}