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382
The Width Of GaltonWatson Trees
, 1999
"... . It is proved that the moments of the width of GaltonWatson trees with offspring variance oe are asymptotically given by (oe p n) p mp where mp are the moments of the maximum of the local time of a standard scaled Brownian excursion. This is done by combining a weak limit theorem and a tightne ..."
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Cited by 3 (3 self)
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. It is proved that the moments of the width of GaltonWatson trees with offspring variance oe are asymptotically given by (oe p n) p mp where mp are the moments of the maximum of the local time of a standard scaled Brownian excursion. This is done by combining a weak limit theorem and a
1 GaltonWatson Trees
"... Exercise 1.1 (Catalan number). 1. Show that there exists a bijection between the set Bn of rooted, oriented binary trees with 2n edges and the set An of rooted, oriented (general) trees with n edges. 2. The generating function of Bn is by definition B(z) = ∑ z 2n #Bn. Show that B satisfies B(z) = ..."
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Exercise 1.1 (Catalan number). 1. Show that there exists a bijection between the set Bn of rooted, oriented binary trees with 2n edges and the set An of rooted, oriented (general) trees with n edges. 2. The generating function of Bn is by definition B(z) = ∑ z 2n #Bn. Show that B satisfies B
Bootstrap percolation on Galton–Watson trees
, 2013
"... Bootstrap percolation is a type of cellular automaton which has been used to model various physical phenomena, such as ferromagnetism. For each natural number r, the rneighbour bootstrap process is an update rule for vertices of a graph in one of two states: ‘infected’ or ‘healthy’. In consecutive ..."
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there exists a tree T with branching number br(T) = b and critical probability pc(T, r) < ɛ. However, this is false if we limit ourselves to the wellstudied family of Galton–Watson trees. We show that for every r ≥ 2 there exists a constant cr> 0 such that if T is a Galton–Watson tree with branching
Bootstrap percolation on GaltonWatson trees
"... Abstract Bootstrap percolation is a type of cellular automaton which has been used to model various physical phenomena, such as ferromagnetism. For each natural number r, the rneighbour bootstrap process is an update rule for vertices of a graph in one of two states: 'infected' or 'h ..."
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> 0 there exists a tree T with branching number br(T ) = b and critical probability p c (T, r) < . However, this is false if we limit ourselves to the wellstudied family of GaltonWatson trees. We show that for every r ≥ 2 there exists a constant c r > 0 such that if T is a GaltonWatson
Rotorrouting on GaltonWatson trees
 ELECTRONIC COMMUNICATIONS IN PROBABILITY
, 2005
"... A rotorrouter walk on a graph is a deterministic process, in which each vertex is endowed with a rotor that points to one of the neighbors. A particle located at some vertex first rotates the rotor in a prescribed order, and then it is routed to the neighbor the rotor is now pointing at. In the cur ..."
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. In the current work we make a step toward in understanding the behavior of rotorrouter walks on random trees. More precisely, we consider random i.i.d. initial configurations of rotors on GaltonWatson trees T, i.e. on a family tree arising from a GaltonWatson process, and give a classification in recurrence
A NOTE ON CONDITIONED GALTONWATSON TREES
"... Abstract. We give a necessary and sufficient condition for the convergence in distribution of a conditioned GaltonWatson tree to Kesten’s tree. This yields elementary proofs of Kesten’s result as well as other known results on local limit of conditioned GaltonWatson trees. We then apply this condi ..."
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Abstract. We give a necessary and sufficient condition for the convergence in distribution of a conditioned GaltonWatson tree to Kesten’s tree. This yields elementary proofs of Kesten’s result as well as other known results on local limit of conditioned GaltonWatson trees. We then apply
Conditioned GaltonWatson trees do not grow
 In Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees Combinatorics and Probability
, 2006
"... An example is given which shows that, in general, conditioned Galton–Watson trees cannot be obtained by adding vertices one by one, while this can be done in some important but special cases, as shown by Luczak and Winkler. Keywords: conditioned Galton–Watson trees, random trees, profile 1 Monotonic ..."
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Cited by 8 (2 self)
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An example is given which shows that, in general, conditioned Galton–Watson trees cannot be obtained by adding vertices one by one, while this can be done in some important but special cases, as shown by Luczak and Winkler. Keywords: conditioned Galton–Watson trees, random trees, profile 1
A CONDITIONING PRINCIPLE FOR GALTONWATSON TREES
"... We show that an infinite GaltonWatson tree, conditioned on its martingale limit being smaller than ε, converges as ε ↓ 0 in law to the regular µary tree, where µ is the essential minimum of the offspring distribution. This gives an example of entropic repulsion where the limit has no entropy. ..."
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We show that an infinite GaltonWatson tree, conditioned on its martingale limit being smaller than ε, converges as ε ↓ 0 in law to the regular µary tree, where µ is the essential minimum of the offspring distribution. This gives an example of entropic repulsion where the limit has no entropy.
Results 1  10
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382