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Lévy master fields on the plane

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This is a joint work with Guillaume Cébron and Franck Gabriel. We shall consider a family of random matrix models introduced by Thierry Lévy and called Markovian holonomy fields. Each of them is characterized by a Lévy process with suitable invariance properties on a compact group of matrices. The Yang-Mills measure on the Euclidean plane can be viewed as such and is characterized by a Brownian motion. We shall explain how to use a result analog to the Kolmogorov continuity theorem to prove convergence theorems as the size of the matrices goes to infinity. We classify the limiting objects obtained in this way and characterize among them the limit associated to the Brownian motion, previously considered by Thierry Lévy and called planar master field.

This talk is part of the Probability series.

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