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Universality in Normal Matrix Models

Mathematical Physics & Probability

Speaker: Roman Riser , ETH-Zurich
Location: 1147 MSB
Start time: Wed, Oct 30 2013, 4:10PM

In the beginning, the basics about random matrix models and some facts about normal random matrices in relation with conformal mappings will be explained. Then we will sketch a proof of universality in Gaus- sian random normal matrices. The proof is based on orthogonal polynomi- als and we are using some new identities which play a similar role as the Christoffel-Darboux formula in Hermitian random matrices. In the limit, when the dimension of the matrices goes to infinity, we will find that the density of eigenvalues is constant inside an ellipse and zero outside. At the boundary, in appropriately scaled coordinates, it will fall off to zero like the complementary error function. We will also consider the off-diagonal part of the kernel and calculate the correlation function. The result will be illustrated by some graphics.