👉 Random Matrix Theory (RMT) is a branch of mathematics that studies the properties and behavior of large random matrices, which are matrices whose entries are random variables. RMT emerged from the intersection of physics, particularly quantum mechanics, and number theory, but it has since found applications across various fields including statistics, finance, and condensed matter physics. The theory provides tools to analyze the statistical properties of eigenvalues (the values that represent the matrix's principal scalars) and eigenvectors (the directions these eigenvalues point in) of these matrices. Key insights from RMT include universal behavior, where certain statistical properties of eigenvalues become independent of the specific matrix entries' distribution, and the use of random matrices to model complex systems and predict their behavior. RMT has proven particularly useful in understanding phenomena like spectral statistics in nuclear physics, financial market volatility, and the behavior of quantum systems.
