  We study numerically various properties of the free energy barriers in the
Edwards-Anderson model of spin glasses in the low-temperature region both in
three and four spatial dimensions. In particular, we investigated the
dependence of height of free energy barriers on system size and on the distance
between the initial and final states (i.e. the overlap distance). A related
quantity is the distribution of large local fluctuations of the overlap in
large three-dimensional samples at equilibrium. Our results for both quantities
(barriers and large deviations) are in agreement with the prediction obtained
in the framework of mean field theory. In addition, our result supports
$D_{lc}=2.5$ as the lower critical dimension for the model.
