A phase transition for the limiting spectral density of random matrices

2012/05/30 by Olga Friesen, Matthias Löwe, Friesen, Olga +1
Mathematics · #60B20 #60F15 #60K35 #Advanced Combinatorial Mathematics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR #msc:60B20 #msc:60F15 #msc:60K35

paper · pdf · doi:10.48550/arxiv.1205.6640

16 pages, 1 figure

arxiv created 2012/05/30 · openalex publication_date 2012/05/30 · arxiv updated 2012/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated. Depending on the strength of correlation the limiting spectral distribution is either the famous semicircle law or some other law, related to that derived for Toeplitz matrices by Bryc, Dembo and Jiang (2006).

Citations

• Random matrices: Universality of local eigenvalue statistics
• On the Distribution of the Roots of Certain Symmetric Matrices

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