Probability theory on Galton-Watson trees
Author(s)Perlin, Alex, 1974-
Massachusetts Institute of Technology. Dept. of Mathematics.
Daniel W. Stroock.
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By a Galton-Watson tree T we mean an infinite rooted tree that starts with one node and where each node has a random number of children independently of the rest of the tree. In the first chapter of this thesis, we prove a conjecture made in  for Galton-Watson trees where vertices have bounded number of children not equal to 1. The conjecture states that the electric conductance of such a tree has a continuous distribution. In the second chapter, we study rays in Galton-Watson trees. We establish what concentration of vertices with is given number of children is possible along a ray in a typical tree. We also gauge the size of the collection of all rays with given concentrations of vertices of given degrees.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.Includes bibliographical references (p. 91).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology