منابع مشابه
Subcritical Galton-Watson Trees
Each variable X is a new, independent Uniform [0, 1] random number. For example, T = ∅ with probability 1−p, T = (∅, ∅) with probability p(1−p)2, and T = ((∅, ∅), ∅) with probability p2(1− p). The number of vertices N is equal to twice the number of left parentheses (parents) in the expression for T , plus one. Equivalently, N is twice the number of ∅s (leaves), minus one. It can be shown that ...
متن کاملThe Width of Galton-watson Trees
It is proved that the moments of the width of Galton-Watson trees with oospring variance are asymptotically given by (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 tightness estimate. The method is quite general and we state some further applications.
متن کاملInformational cascades in Galton-Watson trees
Information cascades have been studied in the literature where myopic selfish users sequentially appear and make a decision to buy a product based on their private observation about the value of the product and actions of their predecessors. Bikhchandani et. al (1992) and Banerjee (1992) introduced such a model and showed that after a finite time almost surely, users discard their private infor...
متن کاملSimulating Size-constrained Galton-Watson Trees
We discuss various methods for generating random Galton-Watson trees conditional on their sizes being equal to n. A linear expected time algorithm is proposed.
متن کاملA Conditioning Principle for Galton–watson Trees
We show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than ε, converges as ε ↓ 0 in law to the regular μ-ary 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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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2019
ISSN: 1083-6489
DOI: 10.1214/19-ejp355