{"paper":{"title":"The density of eigenvalues seen from the soft edge of random matrices in the Gaussian beta-ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Anthony Perret, Gregory Schehr","submitted_at":"2015-05-31T15:28:01Z","abstract_excerpt":"We characterize the phenomenon of \"crowding\" near the largest eigenvalue $\\lambda_{\\max}$ of random $N \\times N$ matrices belonging to the Gaussian $\\beta$-ensemble of random matrix theory, including in particular the Gaussian orthogonal ($\\beta=1$), unitary ($\\beta=2$) and symplectic ($\\beta = 4$) ensembles. We focus on two distinct quantities: (i) the density of states (DOS) near $\\lambda_{\\max}$, $\\rho_{\\rm DOS}(r,N)$, which is the average density of eigenvalues located at a distance $r$ from $\\lambda_{\\max}$ (or the density of eigenvalues seen from $\\lambda_{\\max}$) and (ii) the probabilit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00245","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"}