CLT for spectra of submatrices of Wigner random matrices
classification
🧮 math.PR
math-phmath.MP
keywords
gaussianmatricesspectrasubmatriceswignercollectioncorrelatedentries
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We prove a CLT for spectra of submatrices of real symmetric and Hermitian Wigner matrices. We show that if in the standard normalization the fourth moment of the off-digonal entries is GOE/GUE-like then the limiting Gaussian process can be viewed as a collection of simply yet nontrivially correlated two-dimensional Gaussian Free Fields.
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