• Login
    View Item 
    •   SMARTech Home
    • Georgia Tech Theses and Dissertations
    • Georgia Tech Theses and Dissertations
    • View Item
    •   SMARTech Home
    • Georgia Tech Theses and Dissertations
    • Georgia Tech Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Topics in spatial and dynamical phase transitions of interacting particle systems

    Thumbnail
    View/Open
    restrepolopez_ricardo_201112_phd.pdf (1.108Mb)
    Date
    2011-08-19
    Author
    Restrepo Lopez, Ricardo
    Metadata
    Show full item record
    Abstract
    In this work we provide several improvements in the study of phase transitions of interacting particle systems: - We determine a quantitative relation between non-extremality of the limiting Gibbs measure of a tree-based spin system, and the temporal mixing of the Glauber Dynamics over its finite projections. We define the concept of 'sensitivity' of a reconstruction scheme to establish such a relation. In particular, we focus on the independent sets model, determining a phase transition for the mixing time of the Glauber dynamics at the same location of the extremality threshold of the simple invariant Gibbs version of the model. - We develop the technical analysis of the so-called spatial mixing conditions for interacting particle systems to account for the connectivity structure of the underlying graph. This analysis leads to improvements regarding the location of the uniqueness/non-uniqueness phase transition for the independent sets model over amenable graphs; among them, the elusive hard-square model in lattice statistics, which has received attention since Baxter's solution of the analogous hard-hexagon in 1980. - We build on the work of Montanari and Gerschenfeld to determine the existence of correlations for the coloring model in sparse random graphs. In particular, we prove that correlations exist above the 'clustering' threshold of such a model; thus providing further evidence for the conjectural algorithmic 'hardness' occurring at such a point.
    URI
    http://hdl.handle.net/1853/42729
    Collections
    • Georgia Tech Theses and Dissertations [22401]
    • School of Mathematics Theses and Dissertations [399]

    Browse

    All of SMARTechCommunities & CollectionsDatesAuthorsTitlesSubjectsTypesThis CollectionDatesAuthorsTitlesSubjectsTypes

    My SMARTech

    Login

    Statistics

    View Usage StatisticsView Google Analytics Statistics
    facebook instagram twitter youtube
    • My Account
    • Contact us
    • Directory
    • Campus Map
    • Support/Give
    • Library Accessibility
      • About SMARTech
      • SMARTech Terms of Use
    Georgia Tech Library266 4th Street NW, Atlanta, GA 30332
    404.894.4500
    • Emergency Information
    • Legal and Privacy Information
    • Human Trafficking Notice
    • Accessibility
    • Accountability
    • Accreditation
    • Employment
    © 2020 Georgia Institute of Technology