{"paper":{"title":"Two point eigenvalue correlation for a class of non-selfadjoint operators under random perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Martin Vogel","submitted_at":"2014-12-01T10:40:19Z","abstract_excerpt":"We consider a non-selfadjoint $h$-differential model operator $P_h$ in the semiclassical limit ($h\\rightarrow 0$) subject to random perturbations with a small coupling constant $\\delta$. Assume that $\\exp(-\\frac{1}{Ch}) < \\delta \\ll h^{\\kappa}$ for constants $C,\\kappa>0$ suitably large. Let $\\Sigma$ be the closure of the range of the principal symbol. We study the $2$-point intensity measure of the random point process of eigenvalues of the randomly perturbed operator $P_h^{\\delta}$ and prove an $h$-asymptotic formula for the average $2$-point density of eigenvalues. With this we show that two"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0414","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"}