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The stochastic Lévy Laplacian and Yang-Mills equation on manifolds. (English) Zbl 1049.58037

It is known that a connection on a vector bundle over \(\mathbb{R}^n\) satisfies the Yang-Mills equation if and only if its parallel transport is a zero of its Lévy Laplacian.
This work considers two generalisations of this result. Firstly, the space \(\mathbb{R}^n\) is replaced by a manifold. Secondly, one considers a stochastic framework with stochastic parallel transport and stochastic Lévy Laplacian.

MSC:

58J65 Diffusion processes and stochastic analysis on manifolds
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
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