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Zbl 1049.58037
Léandre, Rémi; Volovich, Igor A.
The stochastic Lévy Laplacian and Yang-Mills equation on manifolds. (English)
[J] Infin. Dimens. Anal. Quantum Probab. Relat. Top. 4, No. 2, 161-172 (2001). ISSN 0219-0257

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

MSC 2000:: *58J65 Diffusion processes and stochastic analysis on manifolds
53C07 Special connections and metrics on vector bundles

Keywords: Lévy Laplacian; Yang-Mills equation

Cited in: Zbl 1155.35482

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