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Abstract: I will discuss the random tiling model of a hexagonal region in the plane with doubly periodic weightings. The model exhibits three asymptotic regimes, known as frozen, rough and smooth. The analysis of the model requires the solution of an extremal problem on the spectral curve that is similar to the equilibrium problem for unitary random matrix ensembles. The extremal problem can be solved for a class of 3 x 3 periodic weightings. Within this class there are two phase transitions.
This is joint work with Max van Horssen.
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Abstract: Before the work of Gernot on the QCD Dirac spectrum, the concept of universality in random matrix theory was largely unknown in the Quantum Chromodynamics community. However, universality was understood in a different way, as the uniqueness of the low-energy effective action, which is determined by symmetries and their spontaneous breaking. We will review these ideas and discuss their connections and implications.
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