  Random forests are notable learning algorithms first introduced by Breinman
in 2001, they are widely used for classification and regression tasks and their
mathematical properties are under ongoing research. We consider a specific
class of random forest algorithms related to kernel methods, the so-called KeRF
(Kernel Random Forests.) In particular, we investigate thoroughly two explicit
algorithms, designed independently of the data set, the centered KeRF and the
uniform KeRF. In the present article, we provide an improvement in the rate of
convergence for both algorithms and we explore the related reproducing kernel
Hilbert space defined by the explicit kernel of the centered random forest.
