Markovian parameters in random trees

In this talk, we look at random trees commonly known as Galton-Watson trees. This species of trees includes, for example,the well-known Cayley trees, Motzkin trees and Catalan trees. With each node in the tree, we associate a random value in a bottom-up manner : the value of a node is a function of the values of the children and possibly an independent random element, hence the name "Markovian". Of particular interest is the behavior of the value of the root as the tree becomes large.  For a given class of such Markovian functions, we analyze the root's value. Applications in computer science, linear programming and  security modeling will be highlighted.