Fluctuations of Linear Eigenvalues Statistics for Wigner Matrices: Edge Case

In this note, we consider the fluctuation theorem for X(n)fn := ∑f(λi)I(λi≥θn), where λi, i=1,…,n are eigenvalues from a Wigner matrix and θn→2−. We prove that in the edge case X(n)fn behaves like the counting function of Wigner matrix. Our results can be viewed as a complement of Bao et al. (J Stat Phys 150(1):88–129, 2013).MOE (Min. of Education, S’pore)Accepted versio