{"paper":{"title":"A pluricomplex error-function kernel at the edge of polynomial Bergman kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Near the droplet edge, polynomial Bergman kernels converge locally to the error-function kernel or a new multivariate version of it.","cross_cats":["math-ph","math.CV","math.MP"],"primary_cat":"math.PR","authors_text":"L. D. Molag","submitted_at":"2026-04-06T13:15:28Z","abstract_excerpt":"We consider polynomial Bergman kernels with respect to exponentially varying weights $e^{-n \\mathscr Q(z)}$ depending on a potential $\\mathscr Q:\\mathbb C^d\\to\\mathbb R$. We use these kernels to construct determinantal point processes on $\\mathbb C^d$. Under mild conditions on the potential, the points are known to accumulate on a compact set $S_{\\mathscr Q}$ called the droplet. We show that the local behavior of the kernel in the vicinity of the edge $\\partial S_{\\mathscr Q}$ is described in two different ways by universal limiting kernels. One of these limiting kernels is the error-function "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that the local behavior of the kernel in the vicinity of the edge ∂S_Q is described in two different ways by universal limiting kernels. One of these limiting kernels is the error-function kernel, which is ubiquitous in random matrix theory, while the other limiting kernel is a new universal object: a multivariate version of the error-function kernel.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The results hold under mild conditions on the potential Q and only in the two qualitatively different settings: (i) the tensorized case where Q decomposes as a sum of planar potentials, and (ii) the case where Q is rotational symmetric.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"At the edge of droplets for polynomial Bergman kernels, local statistics are described by the error-function kernel and a new multivariate error-function kernel in tensorized or rotationally symmetric settings.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Near the droplet edge, polynomial Bergman kernels converge locally to the error-function kernel or a new multivariate version of it.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fdfe37794fee904d9fc267e14f56e41a590334556f794855c1ea2194c0a55e86"},"source":{"id":"2604.04661","kind":"arxiv","version":3},"verdict":{"id":"857962d8-dcd3-43d1-bb9a-7fdf61d188b1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T20:10:36.031843Z","strongest_claim":"We show that the local behavior of the kernel in the vicinity of the edge ∂S_Q is described in two different ways by universal limiting kernels. One of these limiting kernels is the error-function kernel, which is ubiquitous in random matrix theory, while the other limiting kernel is a new universal object: a multivariate version of the error-function kernel.","one_line_summary":"At the edge of droplets for polynomial Bergman kernels, local statistics are described by the error-function kernel and a new multivariate error-function kernel in tensorized or rotationally symmetric settings.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The results hold under mild conditions on the potential Q and only in the two qualitatively different settings: (i) the tensorized case where Q decomposes as a sum of planar potentials, and (ii) the case where Q is rotational symmetric.","pith_extraction_headline":"Near the droplet edge, polynomial Bergman kernels converge locally to the error-function kernel or a new multivariate version of it."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.04661/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"}