{"paper":{"title":"Poisson statistics of eigenvalues in the hierarchical Dyson model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Bendikov, Anton Braverman, John Pike","submitted_at":"2015-10-18T21:50:45Z","abstract_excerpt":"Let $(X,d)$ be a locally compact separable ultrametric space. Given a measure $m$ on $X$ and a function $C$ defined on the set $\\mathcal{B}$ of all balls $B\\subset X$ we consider the hierarchical Laplacian $L=L_{C}$. The operator $L$ acts in $L^{2}(X,m)$, is essentially self-adjoint, and has a purely point spectrum. Choosing a family $\\{\\varepsilon(B)\\}_{B\\in \\mathcal{B}}$ of i.i.d. random variables, we define the perturbed function $\\mathcal{C}(B)=C(B)(1+\\varepsilon(B))$ and the perturbed hierarchical Laplacian $\\mathcal{L}=L_{\\mathcal{C}}$. All outcomes of the perturbed operator $\\mathcal{L}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05312","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"}