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 Maximal Center Gauge (MCG) aims to detect center vortices by maximizing a gauge functional and then projecting onto the center elements of the respective group. The requirement for unrestricted maximization of the gauge functional has proven to be untenable because it was shown that it leads to an underestimation of the string tension. To counter this problem, the ensemble of local gauge maxima is investigated and it is found that the unrestricted maximization can be replaced by a maximization restricted to the Gaussian distributed part of the ensemble. Such restricted maximization weakens the problem of an underestimated string tension. 
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