Network analysis via Random forests

In this thesis we present a strong link between Markov processes and Random forests given a weighted graph. Thanks to Wilson's algorithm we are able cover the graph with a forest and define a probability measure that can sample this method. After proving some important properties regarding random forests, such as the roots set is a determinantal process or that the mean hitting time of the roots set is indipendent from the starting point, we focused on some applications. Random forests are usefull to study metastability of a system via intertwining equations, that is a method to simplify the Markov process associated to this system. At the end we present an application to mean-field models where we want to study how probably two different vertices of the graph will not be connected by a path in the partition given by the forest