Free energies and fluctuations for the Unitary Brownian Motion

Abstract

We show that the Laplace transforms of traces of words in independant unitary Brownian motions converge towards an analytic function on a non trivial disc. This results allow to study asymptotics of Wilson loops under the unitary Yang-Mills measure on the plane. The limiting objects obtained are shown to be characterized by equations analog to Schwinger-Dyson's ones, named here after Makeenko and Migdal.

References in corpus (4)

• Asymptotic expansion of beta matrix models in the one-cut regime
• Monotone Hurwitz numbers in genus zero
• Quantum Free Yang-Mills on the Plane
• Representations of Lie groups and random matrices

Cited by in corpus (7)

• Three proofs of the Makeenko-Migdal equation for Yang-Mills theory on the plane
• The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces
• The generalized master fields
• The large-N limit for two-dimensional Yang-Mills theory
• Large N limit of Yang-Mills partition function and Wilson loops on compact surfaces
• A stochastic PDE approach to large N problems in quantum field theory: a survey
• Wilson loop expectations as sums over surfaces on the plane