👉 Random Matrix Theory (RRM) is a branch of mathematics that studies the properties and applications of random matrices, which are matrices whose entries are random variables. It combines elements from linear algebra, probability theory, and number theory to explore how these matrices behave, especially in large dimensions. RRM has found applications in various fields, including quantum physics, condensed matter physics, and machine learning, by providing insights into the statistical properties of complex systems. Key concepts include eigenvalue distributions, spectral gaps, and universality classes, which help in understanding phenomena like phase transitions and critical behavior in physical systems. The theory also offers tools for analyzing correlations and structures within large datasets, making it a powerful framework for modern scientific research.
