# Random matrix and partial differential equation

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Horng Tzer Yau , Harvard University
Fine Hall 314

It was known that Dyson Brownian motion is closely related to the local statistics of random matrices. In this lecture, I’ll explain that Dyson Brownian motion can be studied by a partial differential equation with random coefficients. From the regularity theory of this PDE, important properties of  local spectral statistics of random matrices can be derived.