Coding multitype forests: application to the law of the total population of branching forests

Loïc Chaumont (1) , Rongli Liu (2)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
2 Department of Mathematics, Nanjing University

By extending the breadth first search algorithm to any $d$-type critical or subcritical irreducible branching tree, we show that such trees may 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 allow us to give an explicit form of the law of the total progeny, jointly with the number of subtrees of each type, in terms of the offspring distribution of the branching process.

Mots clés: cyclic exchangeablity; Multitype branching forest; coding; random walks; ballot theorem; total progeny; cyclic exchangeablity.

Domaines: Probabilités [math.PR]

Loïc Chaumont, Rongli Liu. Coding multitype forests: application to the law of the total population of branching forests. 2013. ⟨hal-00783509v3⟩