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multifractal structure of Galton-Watson trees, and SJ Taylor and X Hu gave a multifractal.

It is tempting to think that the result is‘obvious’, and indeed that a corresponding result should hold for any Galton–Watson process. ... Consider the ‘forward process’ given by ignoring backward children.This is simply a Poisson

sr}. Given i [r] let Xi(resp. Xi ) denote the Galton-Watson process starting at a particle of type si such that thenumber of children of type sk S of a ... β̂f). Remark 16 (Branching process approximation). Consider the multi-type Galton-Watson.

Simply generated trees, conditioned Galton-Watson trees, random alloca-tions and condensation. Probab. ... Surv., 9:103–252, 2012. URL http://dx.doi.org/10.1214/11-PS188. [10] I. Kortchemski. Limit theorems for conditioned non-generic galton-watson

If ξ is Po(r) distributed we call T ξ a Poisson(r) Galton-Watson tree. ... Lemma 6.4 ([29], Lemma 2.1). Let T be a Poisson(r) Galton-Watson tree.

We start by recalling some well-known branching processes results (we include proofs for completeness).Let Xn,p denote a Galton–Watson branching process with Bin(n,p) offspring distribution, starting

Branching Brownian motion (BBM) is a classical process in probability, describing a population of particles performing independent Brownian motion and branching according to a Galton Watson process.

We use these results to obtain new height bounds on conditioned Bienaymé-Galton-Watson trees and simply generated trees.

Random walks on decorated Galton-Watson trees.

I will talk about Galton-Watson trees conditioned on both the total number of vertices $n$ and the number of leaves $k$.