University at Buffalo 3 credits Mechanical & Aerospace Engr
Random matrix theory (RMT) has been successfully used in a diverse field of applications leading to many new modeling concepts and novel parameter estimation techniques. This helps better characterization of uncertainty in complex systems. The course is designed for advanced graduate students and will start by briefly reviewing the measure-theoretic probability covering random variable (RV), random vector, and simulation of RV. It will then focus on the main topics of the course that includes Jaynes’ maximum entropy (MaxEnt) principle, solving MaxEnt optimization problem, concept of random matrix, Gaussian orthogonal/unitary/symplectic ensembles, matrix-variate normal distribution, Wishart distribution, matrix-variate beta distribution, matrix-variate Kummer-beta distribution, simulation of random matrix, and application to some problems of interest (if time permits). Pre-requisite is the course on “Probability Essentials and Applications” described earlier.
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