{"paper":{"title":"Truncated linear statistics associated with the top eigenvalues of 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":"Aur\\'elien Grabsch, Christophe Texier, Satya N. Majumdar","submitted_at":"2016-09-27T07:47:04Z","abstract_excerpt":"Given a certain invariant random matrix ensemble characterised by the joint probability distribution of eigenvalues $P(\\lambda_1,\\ldots,\\lambda_N)$, many important questions have been related to the study of linear statistics of eigenvalues $L=\\sum_{i=1}^Nf(\\lambda_i)$, where $f(\\lambda)$ is a known function. We study here truncated linear statistics where the sum is restricted to the $N_1<N$ largest eigenvalues: $\\tilde{L}=\\sum_{i=1}^{N_1}f(\\lambda_i)$. Motivated by the analysis of the statistical physics of fluctuating one-dimensional interfaces, we consider the case of the Laguerre ensemble"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08296","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"}