Markov chains in Random Matrix Theory

Markov chains in Random Matrix Theory

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Nikita Lvov, Princeton University
Fine Hall 1001

Random Matrix Theory originated in quantum mechanics but the behavior it describes has been observed throughout mathematics, in fields as diverse as number theory, spectral theory and representation theory. I would like to argue that it should be possible to understand these statistics without direct reference to random matrices, by analyzing certain Markov chains, which be will derived.

I will touch upon both the archimedean and non-archimedean side (the structure theorem for p-groups in one case should be viewed as the analogue of the spectral theorem in the other). I will moreover discuss the role played by the Central Limit Theorem.