Abstract
We study weak and strong convergence of the stochastic parallel transport for time → ∞ on Euclidean space. We show that the asymptotic behavior can be controlled by the Yang-Mills action and the Yang-Mills equations. For open paths we show that under appropriate curvature conditions there exits a gauge in which the stochastic parallel transport converges almost surely. For closed paths we show that there exists a gauge invariant notion of a weak limit of the random holonomy and we give conditions that insure the existence of such a limit. Finally, we study the asymptotic behavior of the average of the random holonomy in the case of t'Hooft's 1-instanton.
Original language | English (US) |
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Pages (from-to) | 43-57 |
Number of pages | 15 |
Journal | Potential Analysis |
Volume | 18 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2003 |
ASJC Scopus subject areas
- Analysis