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dc.contributor.advisorPickrell, Douglas
dc.contributor.authorZhou, Wuyin
dc.creatorZhou, Wuyin
dc.date.accessioned2019-06-13T03:51:33Z
dc.date.available2019-06-13T03:51:33Z
dc.date.issued2019
dc.identifier.citationZhou, Wuyin. (2019). Random Walks And Random Self-Avoiding Walks (Bachelor's thesis, University of Arizona, Tucson, USA).
dc.identifier.urihttp://hdl.handle.net/10150/632707
dc.description.abstractIt is well-known that the continuum limit of a random walk on a lattice is Brownian motion. Similarly it is believed (but not known) that the continuum limit of a self-avoiding walk is so called Schramm-Loewner evolution, and that the continuum limit of a random self-avoiding polygon is a random loop measure recently constructed by Wendelin Werner. In this paper we give an exposition of these objects. The main questions we eventually focus on are combinatorial issues regarding numbers of self-avoiding walks and polygons. It is a surprise to find that the connective constant for self-avoiding walks and self-avoiding polygons are the same. Some of these issues have been recently settled by Mardras, Slade, Lawler, Duminil-Copin, Smirnov, and Hammond.
dc.language.isoen
dc.publisherThe University of Arizona.
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.titleRandom Walks And Random Self-Avoiding Walks
dc.typetext
dc.typeElectronic Thesis
thesis.degree.grantorUniversity of Arizona
thesis.degree.disciplineHonors College
thesis.degree.disciplineMathematics
thesis.degree.nameB.A.
refterms.dateFOA2019-06-13T03:51:33Z


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