Probability theory on Galton-Watson trees
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2005
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| Online Access: | http://hdl.handle.net/1721.1/8673 |
| _version_ | 1811070842899005440 |
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| author | Perlin, Alex, 1974- |
| author2 | Daniel W. Stroock. |
| author_facet | Daniel W. Stroock. Perlin, Alex, 1974- |
| author_sort | Perlin, Alex, 1974- |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001. |
| first_indexed | 2024-09-23T08:42:31Z |
| format | Thesis |
| id | mit-1721.1/8673 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T08:42:31Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/86732019-04-09T19:20:22Z Probability theory on Galton-Watson trees Perlin, Alex, 1974- Daniel W. Stroock. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. 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. 2005-08-23T22:13:00Z 2005-08-23T22:13:00Z 2001 2001 Thesis http://hdl.handle.net/1721.1/8673 49650981 eng 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 91 p. 5022615 bytes 5022372 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Perlin, Alex, 1974- Probability theory on Galton-Watson trees |
| title | Probability theory on Galton-Watson trees |
| title_full | Probability theory on Galton-Watson trees |
| title_fullStr | Probability theory on Galton-Watson trees |
| title_full_unstemmed | Probability theory on Galton-Watson trees |
| title_short | Probability theory on Galton-Watson trees |
| title_sort | probability theory on galton watson trees |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/8673 |
| work_keys_str_mv | AT perlinalex1974 probabilitytheoryongaltonwatsontrees |