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arXiv · 2110.15816

Homotopy and holonomy of the planar Brownian motion in a Poisson punctured plane

Isao Sauzedde
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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. In a limit when the number of point grows whilst the singular curvature on each point diminishes, the model converges in some sense towards a Yang--Mills field. We study another regime for which we prove that the holonomy along a Brownian trajectory converges towards an explicit limit.

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Isao Sauzedde. 2021-10-29. Homotopy and holonomy of the planar Brownian motion in a Poisson punctured plane. https://arxiv.org/abs/2110.15816

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