Random matrices are mathematical objects where the entries of the matrix are generated randomly according to specific probability distributions. They are used in various fields, including statistics, quantum physics, and machine learning, to model complex systems and analyze data. The study of random matrices helps researchers understand the behavior of large systems and the properties of their eigenvalues. The theory of random matrices has connections to number theory, graph theory, and statistical mechanics. One of the key results in this area is the Wigner semicircle law, which describes the distribution of eigenvalues for large random matrices. This framework provides insights into phenomena such as phase transitions and chaos in physical systems.