Random forest basic question
I a paper about general algorithm of random forest, it is said on each node, a subset of variables is chosen to test.
my Question: When its constructing the tree with the training set, will there already be made the choice of random variables to built the tree? or will it be trained with all variables, and afterwards, for testing only a small subset of variables will be chosen to test the tree on OOB data?
and finally, do the subsets always have to be nonoverlapping, means distinct from eachother? or is it entirely randomly how to choose variables? so that there can also be repeated variables (more than one of the same) to test each node?