{"paper":{"title":"Distribution of spectral linear statistics on random matrices beyond the large deviation function -- Wigner time delay in multichannel disordered wires","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Aur\\'elien Grabsch, Christophe Texier","submitted_at":"2016-02-10T13:45:18Z","abstract_excerpt":"An invariant ensemble of $N\\times N$ random matrices can be characterised by a joint distribution for eigenvalues $P(\\lambda_1,\\cdots,\\lambda_N)$. The study of the distribution of linear statistics, i.e. of quantities of the form $L=(1/N)\\sum_if(\\lambda_i)$ where $f(x)$ is a given function, appears in many physical problems. In the $N\\to\\infty$ limit, $L$ scales as $L\\sim N^\\eta$, where the scaling exponent $\\eta$ depends on the ensemble and the function $f$. Its distribution can be written under the form $P_N(s=N^{-\\eta}\\,L)\\simeq A_{\\beta,N}(s)\\,\\exp\\big\\{-(\\beta N^2/2)\\,\\Phi(s)\\big\\}$, wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03370","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"}