| dc.identifier.uri | http://hdl.handle.net/11401/76413 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.abstract | ABSTRACT. Oriented loops on an orientable surface are, up to equivalence by free homotopy, in one-to-one correspondence with the conjugacy classes of the surface's fundamental group. These conjugacy classes can be expressed (not uniquely in the case of closed surfaces) as a cyclic word of minimal length in terms of the fundamental group's generators. The self-intersection number of a conjugacy class is the minimal number of transverse self-intersections of representatives of the class. By using Markov chains to encapsulate the exponential mixing of the geodesic flow and achieve sufficient independence, we can use a form of the central limit theorem to describe the statistical nature of the self-intersection number. For a class chosen at random among all classes of length n, the distribution of the self intersection number approaches a Gaussian when n is large. This theorem generalizes the result of Steven Lalley and Moira Chas to include the case of closed surfaces. | |
| dcterms.available | 2017-09-20T16:50:11Z | |
| dcterms.contributor | Chas, Moira | en_US |
| dcterms.contributor | Milnor, John | en_US |
| dcterms.contributor | Rocek, Martin. | en_US |
| dcterms.contributor | Sullivan, Dennis | en_US |
| dcterms.creator | Wroten, Matthew Murray | |
| dcterms.dateAccepted | 2017-09-20T16:50:11Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:11Z | |
| dcterms.description | Department of Mathematics. | en_US |
| dcterms.extent | 41 pg. | en_US |
| dcterms.format | Application/PDF | en_US |
| dcterms.format | Monograph | |
| dcterms.identifier | http://hdl.handle.net/11401/76413 | |
| dcterms.issued | 2013-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:11Z (GMT). No. of bitstreams: 1
Wroten_grad.sunysb_0771E_11495.pdf: 476244 bytes, checksum: 60770341bbaf091687a17e26e0f191a6 (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Dynamics, Gaussian, Intersection, Statistics, Surface, Topology | |
| dcterms.subject | Mathematics | |
| dcterms.title | The Eventual Gaussian Distribution of Self-Intersection Numbers on Closed Surfaces | |
| dcterms.type | Dissertation | |
