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

Abstract : 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.
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Cited literature [13 references]

https://hal.archives-ouvertes.fr/hal-00783509
Contributor : Loïc Chaumont Connect in order to contact the contributor
Submitted on : Thursday, March 13, 2014 - 10:34:42 AM
Last modification on : Wednesday, October 20, 2021 - 3:18:47 AM
Long-term archiving on: : Friday, June 13, 2014 - 11:05:13 AM

### File

cl1.pdf
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### Identifiers

• HAL Id : hal-00783509, version 3

### Citation

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

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