2016/04/30 by Oskari Ajanki, Oskari H. Ajanki, László Erdős +2 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Eigenvalues and eigenvectors #Hermitian matrix #Limit (mathematics) #Matrix (chemical analysis) #Quantum Information and Cryptography #Random Matrices and Applications #Random matrix #Resolvent #Spectral Theory in Mathematical Physics #Stability (learning theory) #Universality (dynamical systems) #math-ph #math.MP #math.PR #msc:15B52 #msc:46T99 #msc:60B20
paper · pdf · doi:10.1007/s00440-018-0835-z
Format was adjusted to coincide with the published version in PTRF
openalex created_date 2016/12/16 · openalex publication_date 2018/02/17 · arxiv created 2018/02/28 · arxiv updated 2018/03/01 · openalex updated_date 2026/08/05
We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent.