Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001. / Includes bibliographical references (p. 91). / 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 [7] 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. / by Alex Perlin. / Ph.D.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/8673 |
| Date | January 2001 |
| Creators | Perlin, Alex, 1974- |
| Contributors | Daniel W. Stroock., Massachusetts Institute of Technology. Dept. of Mathematics., Massachusetts Institute of Technology. Dept. of Mathematics. |
| Publisher | Massachusetts Institute of Technology |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 91 p., 5022615 bytes, 5022372 bytes, application/pdf, application/pdf, application/pdf |
| Rights | M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission., http://dspace.mit.edu/handle/1721.1/7582 |
Page generated in 0.1995 seconds