{"paper":{"title":"Universality of a family of Random Matrix Ensembles with logarithmic soft-confinement potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.dis-nn","authors_text":"Jinmyung Choi, K.A. Muttalib","submitted_at":"2010-06-06T21:49:04Z","abstract_excerpt":"Recently we introduced a family of $U(N)$ invariant Random Matrix Ensembles which is characterized by a parameter $\\lambda$ describing logarithmic soft-confinement potentials $V(H) \\sim [\\ln H]^{(1+\\lambda)} \\:(\\lambda>0$). We showed that we can study eigenvalue correlations of these \"$\\lambda$-ensembles\" based on the numerical construction of the corresponding orthogonal polynomials with respect to the weight function $\\exp[- (\\ln x)^{1+\\lambda}]$. In this work, we expand our previous work and show that: i) the eigenvalue density is given by a power-law of the form $\\rho(x) \\propto [\\ln x]^{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1141","kind":"arxiv","version":3},"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"}