Random matrix theory (RMT) has a long and rich history and has, in recent years, shown to have significant applications in a wide range of fields. It was first introduced due to its profound applications in multivariate statistics, theoretical physics, and other disciplines. The matrix distributions being studied are universal and can be used for statistical simulation and the modeling of physical systems, such as many-body quantum systems and chaotic dynamics.

With increasing research into random matrices in mathematical models and engineering, many new results have emerged both in theory and in practical applications. Currently, these are being used extensively in chaotic systems, nuclear physics, classical analysis, probability theory, image processing, compressed sensing, and statistical analysis of big data, as well as connections to graph theory, number theory and representation theory, among many other areas of mathematical modeling and engineering. In addition, the distribution of synapses in neurons, trees in rainforests, waiting time between buses, securities trading prices, and associations in large random networks can all be described by random matrix statistics.

The aim of this Special Issue is to report the latest theoretical and practical achievements on random matrices in mathematical modeling and engineering to help reach the full potential of random matrices. We welcome original research and review papers on both theories and practical applications which effectively apply RMT to different engineering fields. Orthogonal polynomial theory, free probability, integrable systems, growth models, high-dimensional data analysis, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory are just a few of the fields that fall under this category.

Potential topics include but are not limited to the following:

• New theories of random matrices in mathematical models and engineering applications
• Universality of random matrix dynamics
• Modeling and simulation based on random matrices
• Multivariate statistical analysis based on random matrices
• Deep learning methods based on nonlinear random matrices
• Random matrix theory in feature extraction and neural networks
• Random matrix theory in signal and image processing