Random Matrix Theory
Random Matrix Theory (RMT) is a mathematical framework that studies the properties of matrices with random elements. It originated in the field of statistical physics but has since found applications in various areas, including number theory, quantum mechanics, and machine learning. RMT helps researchers understand complex systems by analyzing the statistical behavior of eigenvalues and eigenvectors of large random matrices.
One of the key insights of RMT is that certain statistical properties of eigenvalues, such as their distribution, can be predicted regardless of the specific details of the matrix. This has led to significant advancements in understanding phenomena in nuclear physics, wireless communication, and even finance, where complex systems can be modeled using random matrices.