The master field on the plane

报告题目The master field on the plane


报告人Thierry Levy (巴黎六大)






摘要The Yang-Mills field on the plane is a collection of random matrices indexed by the set of loops based at the origin on the plane. These matrices belong to a fixed compact group, for example the unitary group U(N), and the Yang-Mills field can be thought of as a random unitary representation of the group of rectifiable loops on the plane, the group operation being concatenation. I will describe the large N limit of this random reprensentation, in particular the fact that it converges almost surely towards a deterministic limit. This limit, which is an instance of what physicists call the master field, takes the form of a plain deterministic real-valued function on the set of loops. This function can be computed by a recursive algorithm based on the so-called Makeenko-Migdal equations, which are a graphical translation of the algebraic structure of freeness.


报告人简介Thierry Levy 教授,现任法国巴黎六大教授,曾在法国CNRSStrasbourg)和巴黎高师任职。主要研究领域包括Yang-Mills测度,随机过程、随机场,紧Lie群中的热核问题等。




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