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236
LOCAL DIMENSIONS OF THE BRANCHING MEASURE ON A GALTON–WATSON TREE
, 2001
"... Let µ = µω be the branching measure on the boundary ∂T of a supercritical Galton–Watson tree T = T(ω). Denote by d(µ,u) and d(µ,u) the lower and upper local dimensions of µ at u ∈ ∂T. It is well known that almost surely, d(µ,u) = d(µ,u) = logm for µalmost all u ∈ ∂T, where m is the expected valu ..."
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Cited by 14 (0 self)
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Let µ = µω be the branching measure on the boundary ∂T of a supercritical Galton–Watson tree T = T(ω). Denote by d(µ,u) and d(µ,u) the lower and upper local dimensions of µ at u ∈ ∂T. It is well known that almost surely, d(µ,u) = d(µ,u) = logm for µalmost all u ∈ ∂T, where m is the expected
Thin and thick points for branching measure on a GaltonWatson tree
"... Suppose that µ is the branching measure on the boundary of a supercritical GaltonWatson tree with offspring distribution N such that E[N log + N ] < 1. We determine the dimension spectrum of thin points under the condition PfN 1g = 0 and the dimension spectrum of thick points under the condit ..."
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Cited by 9 (4 self)
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Suppose that µ is the branching measure on the boundary of a supercritical GaltonWatson tree with offspring distribution N such that E[N log + N ] < 1. We determine the dimension spectrum of thin points under the condition PfN 1g = 0 and the dimension spectrum of thick points under
Random walks on Galton–Watson trees with random conductances, Stochastic Process
 Appl
"... Abstract We consider the random conductance model, where the underlying graph is an infinite supercritical GaltonWatson tree, the conductances are independent but their distribution may depend on the degree of the incident vertices. We prove that, if the mean conductance is finite, there is a dete ..."
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Cited by 5 (0 self)
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Abstract We consider the random conductance model, where the underlying graph is an infinite supercritical GaltonWatson tree, the conductances are independent but their distribution may depend on the degree of the incident vertices. We prove that, if the mean conductance is finite, there is a
Effective resistance of random trees
, 2008
"... We investigate the effective resistance Rn and conductance Cn between the root and leaves a binary tree of height n. In this electrical network, the resistance of each an edge e at distance d from the root is defined by re = 2 d Xe where the Xe are i.i.d. positive random variables bounded away from ..."
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zero and infinity. It is shown that ERn = nEXe − (Var(Xe)/EXe) ln n + O(1) and Var(Rn) = O(1). Some of the results are extended to the case when the underlying tree is a supercritical Galton–Watson tree. (In this case the correct scale for re is b d Xe where b is the branching number of the tree.) 1
Wired cyclebreaking dynamics for uniform spanning forests
"... Abstract. We prove that every component of the wired uniform spanning forest (WUSF) is oneended almost surely in every transient reversible random graph, removing the bounded degree hypothesis required by earlier results. We deduce that every component of the WUSF is oneended almost surely in ev ..."
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Cited by 1 (1 self)
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in every supercritical GaltonWatson tree, answering a question of Benjamini, Lyons, Peres and Schramm [3]. Our proof introduces and exploits a family of Markov chains under which the oriented WUSF is stationary, which we call the wired cyclebreaking dynamics. 1.
Survival of inhomogeneous GaltonWatson processes
, 2008
"... We study survival properties of inhomogeneous GaltonWatson processes. We determine the socalled branching number (which is the reciprocal of the critical value for percolation) for these random trees (conditioned on being infinite), which turns out to be an a.s. constant. We also shed some light o ..."
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Cited by 3 (1 self)
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We study survival properties of inhomogeneous GaltonWatson processes. We determine the socalled branching number (which is the reciprocal of the critical value for percolation) for these random trees (conditioned on being infinite), which turns out to be an a.s. constant. We also shed some light
Random walks on GaltonWatson trees: averaging and uncertainty
, 2000
"... Consider a supercritical branching process, with each particle producing at least one child. Starting from rst ancestor (called the root), it denes the GaltonWatson measure GW on rooted innite trees. Let Xn be a simple random walk on a xed rooted tree T drawn from GW, and jXn j the associated dista ..."
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Consider a supercritical branching process, with each particle producing at least one child. Starting from rst ancestor (called the root), it denes the GaltonWatson measure GW on rooted innite trees. Let Xn be a simple random walk on a xed rooted tree T drawn from GW, and jXn j the associated
On the transience of processes defined on GaltonWatson trees
 ANN. PROBAB
, 2006
"... We introduce a simple technique for proving the transience of certain processes defined on the random tree G generated by a supercritical branching process. We prove the transience for oncereinforced random walks on G, that is, a generalization of a result of Durrett, Kesten and Limic [Probab. Theo ..."
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Cited by 9 (3 self)
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We introduce a simple technique for proving the transience of certain processes defined on the random tree G generated by a supercritical branching process. We prove the transience for oncereinforced random walks on G, that is, a generalization of a result of Durrett, Kesten and Limic [Probab
Hausdorff dimension of a Galton–Watson tree
, 1998
"... Abstract. Let T be the genealogical tree of a supercritical multitype Galton–Watson process, and let � be the limit set of T, i.e., the set of all infinite selfavoiding paths (called ends) through T that begin at a vertex of the first generation. The limit set � is endowed with the metric d(ζ,ξ) = ..."
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Abstract. Let T be the genealogical tree of a supercritical multitype Galton–Watson process, and let � be the limit set of T, i.e., the set of all infinite selfavoiding paths (called ends) through T that begin at a vertex of the first generation. The limit set � is endowed with the metric d
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
Results 1  10
of
236