Clay Mathematics Institute

Dedicated to increasing and disseminating mathematical knowledge

Gaussian Free Field in beta ensembles and random surfaces

Alexei Borodin (Massachusetts University of Technology)

Abstract:  The goal of the talk is to argue that the two-dimensional Gaussian Free Field is a universal and unifying object for global fluctuations of spectra of random matrices and random surfaces. This viewpoint leads to natural Gaussian processes on larger spaces which, despite their explicit covariance structure, so far lack conceptual understanding.