2026-09-25T01:40:56Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/86732022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Daniel W. Stroock.
Perlin, Alex, 1974-
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2005-08-23T22:13:00Z
2005-08-23T22:13:00Z
2001
2001
http://hdl.handle.net/1721.1/8673
49650981
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.
91 p.
5022615 bytes
5022372 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Probability theory on Galton-Watson trees
Thesis
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Publication
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