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Large N asymptotics of the Yang-Mills measure

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I will discuss some results and some open problems related to the behaviour of the Yang-Mills measure on compact surfaces as the size of the structure group tends to infinity. The Yang-Mills measure on a compact surface is a collection of random unitary matrices indexed by the space of loops on the surface. The distribution of these random matrices is governed by the properties of the Brownian motion on the unitary group and by the topology of the surface. As for many other matrix models, the Yang-Mills measure has a non-trivial limit as the order of the unitary group tends to infinity, or at least it is strongly believed to have one. On the plane, it is possible to prove that this limit exists and to describe it in a computationally fairly efficient way. Physicists make a number of fantastic predictions on this limit and if time permits I will mention some of them.

This talk is part of the Probability series.

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