{"paper":{"title":"Phase transitions and edge scaling of number variance in Gaussian random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Gr\\'egory Schehr, Pierpaolo Vivo, Ricardo Marino, Satya N. Majumdar","submitted_at":"2014-04-02T14:44:50Z","abstract_excerpt":"We consider $N\\times N$ Gaussian random matrices, whose average density of eigenvalues has the Wigner semi-circle form over $[-\\sqrt{2},\\sqrt{2}]$. For such matrices, using a Coulomb gas technique, we compute the large $N$ behavior of the probability $\\mathcal{P}_{\\scriptscriptstyle N,L}(N_L)$ that $N_L$ eigenvalues lie within the box $[-L,L]$. This probability scales as $\\mathcal{P}_{\\scriptscriptstyle N,L}(N_L=\\kappa_L N)\\approx\\exp\\left(-{\\beta} N^2 \\psi_L(\\kappa_L)\\right)$, where $\\beta$ is the Dyson index of the ensemble and $\\psi_L(\\kappa_L)$ is a $\\beta$-independent rate function that w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0575","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"}