{"paper":{"title":"Berezin-Toeplitz operators, Kodaira maps, and random sections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR","math.SG"],"primary_cat":"math.CV","authors_text":"Michele Ancona (IRMA), Yohann Le Floch (IRMA)","submitted_at":"2022-06-30T08:17:33Z","abstract_excerpt":"We study the zeros of sections of the form $T_k s_k$ of a large power $L^{\\otimes k} \\to M$ of a holomorphic positive Hermitian line bundle over a compact K\\''ahler manifold $M$, where $s_k$ is a random holomorphic section of $L^{\\otimes k}$ and $T_k$ is a Berezin-Toeplitz operator, in the limit $k \\to +\\infty$. In particular, we compute the second order approximation of the expectation of the distribution of these zeros. In a ball of radius of order $k^{-\\frac{1}{2}}$ around $x \\in M$, assuming that the principal symbol $f$ of $T_k$ is real-valued and vanishes transversally, we show that this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.15112","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/2206.15112/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"}