In this paper, we consider the universality of the local eigenvalue statistics of random matrices. Our main result shows that these statistics are determined by the first four moments of the distribution of the entries. As a consequence, we derive the universality of eigenvalue gap distribution and$k$-point correlation, and many other statistics (under some mild assumptions) for both Wigner Hermitian matrices and Wigner real symmetric matrices.

We propose a deep learning-based method for object detection in UAV-borne thermal images that have the capability of observing scenes in both day and night. Compared with visible images, thermal images have lower requirements for illumination conditions, but they typically have blurred edges and low contrast. Using a boundary-aware salient object detection network, we extract the saliency maps of the thermal images to improve the distinguishability. Thermal images are augmented with the corresponding saliency maps through channel replacement and pixel-level weighted fusion methods. Considering the limited computing power of UAV platforms, a lightweight combinational neural network ComNet is used as the core object detection method. The YOLOv3 model trained on the original images is used as a benchmark and compared with the proposed method. In the experiments, we analyze the detection performances of the ComNet models with different image fusion schemes. The experimental results show that the average precisions (APs) for pedestrian and vehicle detection have been improved by 2%~5% compared with the benchmark without saliency map fusion and MobileNetv2. The detection speed is increased by over 50%, while the model size is reduced by 58%. The results demonstrate that the proposed method provides a compromise model, which has application potential in UAV-borne detection tasks.

In this paper we prove the universality of covariance matrices of the form $H_{Ntimes N}={X}^{dagger}X$ where $X$ is an ${Mtimes N}$ rectangular matrix with independent real valued entries $x_{ij}$ satisfying $mathbb{E}x_{ij}=0$ and $mathbb{E}x^2_{ij}={frac{1}{M}}$, $N$, $Mto infty$. Furthermore it is assumed that these entries have sub-exponential tails or sufficiently high number of moments. We will study the asymptotics in the regime $N/M=d_Nin(0,infty),lim_{Ntoinfty}d_Nneq0,infty$. Our main result is the edge universality of the sample covariance matrix at both edges of the spectrum. In the case $lim_{Ntoinfty}d_N=1$, we only focus on the largest eigenvalue. Our proof is based on a novel version of the Green function comparison theorem for data matrices with dependent entries. En route to proving edge universality, we establish that the Stieltjes transform of the empirical eigenvalue distribution of $H$ is given by the Marcenko-Pastur law uniformly up to the edges of the spectrum with an error of order $(Neta)^{-1}$ where $eta$ is the imaginary part of the spectral parameter in the Stieltjes transform. Combining these results with existing techniques we also show bulk universality of covariance matrices. All our results hold for both real and complex valued entries.