Department Seminars & Colloquia
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In the arena of stochastic learning, Mathematics played a crucial role in laying out infrastructures for the arena. We will see pieces of historic evidence of the role. The lecture will mostly be in plain words. The topics in the lecture includes the basic notions of probability, backward reasoning, graph theory, and random graph, and the current status quo of the random graphs will be presented in a variety of forms.
We survey some results in random matrix theory and their universal nature. For instance, consider the largest eigenvalue of a randomly chosen Hermitian matrix. This random variable converges to a certain distribution as the dimension becomes large. It was proved by many different researchers over the last twenty years that this distribution also describes many different models in probability which do not have an apparent connection to matrices. The examples include Coulomb gas, random tilings of a hexagon, random growth models, and directed polymers among others. We will discuss this fascinating university aspect of random matrix theory through several examples.