Seminar in probability theory: Lisa Hartung (New York University)

The Ginibre ensemble and Gaussian multiplicative chaos

It was proven by Rider and Virag that the logarithm of the characteristic polynomial of the Ginibre ensemble converges to a logarithmically correlated random field. In this talk we will see how this connection can be established on the level if powers of the characteristic polynomial by proving convergence to Gaussian multiplicative chaos. We consider the range of powers in the L^2 phase.

(Joint work in progress with Paul Bourgade and Guillaume Dubach).

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