{"paper":{"title":"Scaling of the Reduced Energy Spectrum of Random Matrix Ensemble","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"M. N. Chen, Wen-Jia Rao","submitted_at":"2020-06-14T02:50:40Z","abstract_excerpt":"We study the reduced energy spectrum $\\{E_{i}^{(n)}\\}$, which is constructed by picking one level from every $n$ levels of the original spectrum $\\{E_{i}\\}$, in a Gaussian ensemble of random matrix with Dyson index $\\beta\\in \\left( 0,\\infty \\right) $. It's shown $\\{E_{i}^{(n)}\\}$ bears the same form of probability distribution as $\\{E_{i}\\}$ with a rescaled parameter $\\gamma =\\frac{n(n+1)}{2}\\beta +n-1$. Notably, the $n$-th order level spacing and non-overlapping gap ratio in $\\{E_{i}\\}$ become the lowest-order ones in $\\{E_{i}^{(n)}\\}$, hence their distributions will rescale in an identical w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.07774","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.07774/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}