{"paper":{"title":"Central Limit theorem for spectral Partial Bergman kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.CV","authors_text":"Peng Zhou, Steve Zelditch","submitted_at":"2017-08-30T13:43:18Z","abstract_excerpt":"Partial Bergman kernels $\\Pi_{k, E}$ are kernels of orthogonal projections onto subspaces $\\mathcal{k} \\subset H^0(M, L^k)$ of holomorphic sections of the $k$th power of an ample line bundle over a Kahler manifold $(M, \\omega)$. The subspaces of this article are spectral subspaces $\\{\\hat{H}_k \\leq E\\}$ of the Toeplitz quantization $\\hat{H}_k$ of a smooth Hamiltonian $H: M \\to \\mathbb{R}$. It is shown that the relative partial density of states $\\frac{\\Pi_{k, E}(z)}{\\Pi_k(z)} \\to {1}_{\\mathcal{A}}$ where $\\mathcal{A} = \\{H < E\\}$. Moreover it is shown that this partial density of states exhibi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09267","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"}