{"paper":{"title":"The extremal process of critical points of the pure $p$-spin spherical spin glass model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eliran Subag, Ofer Zeitouni","submitted_at":"2015-09-10T11:18:26Z","abstract_excerpt":"Recently, sharp results concerning the critical points of the Hamiltonian of the $p$-spin spherical spin glass model have been obtained by means of moments computations. In particular, these moments computations allow for the evaluation of the leading term of the ground-state, i.e., of the global minimum. In this paper, we study the extremal point process of critical points - that is, the point process associated to all critical values in the vicinity of the ground-state. We show that the latter converges in distribution to a Poisson point process of exponential intensity. In particular, we id"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03098","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"}