{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"The Eventual Gaussian Distribution of Self-Intersection Numbers on Closed Surfaces","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree."},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/11401/76413"},{"label":"dc.language.iso","value":"en_US"},{"label":"dc.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.abstract","value":"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."},{"label":"dcterms.available","value":"2017-09-20T16:50:11Z"},{"label":"dcterms.contributor","value":"Sullivan, Dennis"},{"label":"dcterms.creator","value":"Wroten, Matthew Murray"},{"label":"dcterms.dateAccepted","value":"2017-09-20T16:50:11Z"},{"label":"dcterms.dateSubmitted","value":"2017-09-20T16:50:11Z"},{"label":"dcterms.description","value":"Department of Mathematics."},{"label":"dcterms.extent","value":"41 pg."},{"label":"dcterms.format","value":"Monograph"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/76413"},{"label":"dcterms.issued","value":"2013-12-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2017-09-20T16:50:11Z (GMT). No. of bitstreams: 1\nWroten_grad.sunysb_0771E_11495.pdf: 476244 bytes, checksum: 60770341bbaf091687a17e26e0f191a6 (MD5)\n  Previous issue date:    1"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"Dynamics, Gaussian, Intersection, Statistics, Surface, Topology"},{"label":"dcterms.title","value":"The Eventual Gaussian Distribution of Self-Intersection Numbers on Closed Surfaces"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/11%2F07%2F98%2F110798918007485174796248129774112757586/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/11%2F07%2F98%2F110798918007485174796248129774112757586","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}