TY - JOUR T1 - The Application of Random Matrices in Mathematical Physics AU - Guo , Boling AU - Li , Fangfang JO - Annals of Applied Mathematics VL - 3 SP - 221 EP - 238 PY - 2022 DA - 2022/06 SN - 33 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/20607.html KW - random matrices, Riemann Hypothesis, Riemann-Hilbert problem, nuclear physics. AB -

In this paper, we introduce the application of random matrices in mathematical physics including Riemann-Hilbert problem, nuclear physics, big data, image processing, compressed sensing and so on. We start with the Riemann-Hilbert problem and state the relation between the probability distribution of nontrivial zeros and the eigenvalues of the random matrices. Through the random matrices theory, we derive the distribution of Neutron width and probability density between energy levels. In addition, the application of random matrices in quantum chromo dynamics and two dimensional Einstein gravity equations is also presented in this paper.