Central Limit Theorem for Linear Eigenvalue Statistics for Submatrices of Wigner Random Matrices
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Central Limit Theorem for Linear Eigenvalue Statistics for Submatrices of Wigner Random Matrices

  • Author(s): Li, Lingyun
  • Reed, Matthew
  • Soshnikov, Alexander
  • et al.

Published Web Location

https://arxiv.org/pdf/1504.05933.pdf
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Abstract

We prove the Central Limit Theorem for finite-dimensional vectors of linear eigenvalue statistics of submatrices of Wigner random matrices under the assumption that test functions are sufficiently smooth. We connect the asymptotic covariance to a family of correlated Gaussian Free Fields.

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