Holonomy of the Planar Brownian Motion in a Poisson Punctured Plane

Abstract We define a family of diffeomorphism-invariant models of random connections on principal G -bundles over the plane, whose curvatures are concentrated on singular points. We study the limit when the number of points grows to infinity whilst the singular curvature on each point diminishes, and prove that the holonomy along a Brownian trajectory converges towards an explicit limit.