{"paper":{"title":"Central Limit theorem for toric \\kahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.PR","authors_text":"Peng Zhou, Steve Zelditch","submitted_at":"2018-02-23T12:25:08Z","abstract_excerpt":"Associated to the Bergman kernels of a polarized toric \\kahler manifold $(M, \\omega, L, h)$ are sequences of measures $\\{\\mu_k^z\\}_{k=1}^{\\infty}$ parametrized by the points $z \\in M$. For each $z$ in the open orbit, we prove a central limit theorem for $\\mu_k^z$. The center of mass of $\\mu_k^z$ is the image of $z$ under the moment map; after re-centering at $0$ and dilating by $\\sqrt{k}$, the re-normalized measure tends to a centered Gaussian whose variance is the Hessian of the \\kahler potential at $z$. We further give a remainder estimate of Berry-Esseen type. The sequence $\\{\\mu_k^z\\}$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08501","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1802.08501/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"}