{"paper":{"title":"Mod-$\\phi$ convergence, II: Estimates on the speed of convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ashkan Nikeghbali, Pierre-Lo\\\"ic M\\'eliot, Valentin F\\'eray","submitted_at":"2017-05-30T07:34:28Z","abstract_excerpt":"In this paper, we give estimates for the speed of convergence towards a limiting stable law in the recently introduced setting of mod-$\\phi$ convergence. Namely, we define a notion of zone of control, closely related to mod-$\\phi$ convergence, and we prove estimates of Berry-Esseen type under this hypothesis. Applications include: the winding number of a planar Brownian motion; classical approximations of stable laws by compound Poisson laws; examples stemming from determinantal point processes (characteristic polynomials of random matrices and zeroes of random analytic functions); sums of var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10485","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":""},"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"}