Large N asymptotics of the YangMills measure
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I will discuss some results and some open problems related to the
behaviour of the YangMills measure on compact surfaces as the size of
the structure group tends to infinity.
The YangMills 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 YangMills measure has a
nontrivial 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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