Gaussian fluctuation for linear eigenvalue statistics of large dilute Wigner matrices

This paper focuses on the dilute real symmetric Wigner matrix $M_n = frac{1} {{sqrt n }}left( {a_{ij} } right)_{n times n}$ , whose offdiagonal entries a _ij (1 ? i ≠ j ? n) have mean zero and unit variance, Ea _ij ⁴ = θn ^α (θ > 0) and the fifth moments of a _ij satisfy a Lindeberg type condition. When the dilute parameter $0 < alpha leqslant tfrac{1} {3}$ and the test function satisfies some regular conditions, it proves that the centered linear eigenvalue statistics of M _n obey the central limit theorem.