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    Random Walks And Random Self-Avoiding Walks

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    Author
    Zhou, Wuyin
    Issue Date
    2019
    Advisor
    Pickrell, Douglas
    
    Metadata
    Show full item record
    Publisher
    The University of Arizona.
    Rights
    Copyright © 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.
    Abstract
    It 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.
    Type
    text
    Electronic Thesis
    Degree Name
    B.A.
    Degree Program
    Honors College
    Mathematics
    Degree Grantor
    University of Arizona
    Collections
    Honors Theses

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