Coding multitype forests: Application to the law of the total population of branching forests
Coding multitype forests: Application to the law of the total population of branching forests
By extending the breadth first search algorithm to any $d$-type critical or subcritical irreducible branching forest, we show that such forests can be encoded through $d$ independent, integer valued, $d$-dimensional random walks. An application of this coding, together with a multivariate extension of the Ballot Theorem which is obtained here, …