Fluctuations of Functions of Wigner Matrices

Abstract

We show that matrix elements of functions of $N\times N$ Wigner matrices fluctuate on a scale of order $N^{-1/2}$ and we identify the limiting fluctuation. Our result holds for any function $f$ of the matrix that has bounded variation and thus considerably relaxes the regularity requirement imposed in [7,11].

Corrected a typo in the definition of X in Section 4. 13 pages

References in corpus (1)

• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries

Cited by in corpus (3)

• Fluctuations of interlacing sequences
• Dynamics of a rank-one perturbation of a Hermitian matrix
• A Quantized Analogue of the Markov-Krein Correspondence