Percolación en árboles de Cayley

Abstract

Percolation is one of the simplest models in the theory of probability that exhibits what is known as critical phenomena, this generally means that there is a natural parameter in the model in which the behavior of the system changes dramatically. In the standard model of percolation theory, the d-dimensional lattice is considered to be the graph consisting of the set Z^d as vertices along with a link between two points that have a Euclidean distance 1. Then it is fixed a parameter p and it is stated that each link in this graph must be opened with probability p and inquire about the structure of the random subgraph obtained consisting of Z^d together with the set of open links. On the other hand, if graphs with certain specifications are considered, the original model is subjected to pre-established conditions, therefore, a new percolation model. One type of graph is called Cayley trees.