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  • Stability Analysis of Coupled Discrete Time Systems On an Invariant Cone

    Creator:
    Fletcher, Sally
    Abstract:
    This paper concerns a question that frequently occurs in various applications: Is any dispersal coupling of stable discrete linear systems, also stable? Although it has been known this is not the case, we shall identify a reasonably diverse class of systems for which it is true. We shall employ the...
    Resource Type:
    Masters Thesis

  • On Invariant Galton-Watson Trees with Exponential Edge Lengths

    Creator:
    Xu, Guochen
    Resource Type:
    Dissertation
    Full Text:
    Professors Enrique Thomann, Elaine Cozzi, Radu Dascaliuc, and Lan Xue for being on my defense committee, and

  • Proving Limit Theorems for Associated Random Variables via Stein's Method

    Creator:
    Jantai, Wasamon
    Abstract:
    Stein's method initially introduced in 1970 by C. Stein is a powerful technique for bounding the distance between the laws of two real-valued random variables. Stein's method has been used to prove distributional convergence to many standard probability distributions such as normal, multivariate normal, Poisson and Brownian motion approximation. In...
    Resource Type:
    Dissertation
    Full Text:
    thesis. Sincere thanks are extended to my dissertation committee, Prof. Enrique A. Thomann, Prof. Radu

  • Aggregate Path Coupling for the Generalized Curie-Weiss Model

    Creator:
    Barbosa, Bruno
    Abstract:
    The topic of statistical mechanics has been studied for over a century, and it is one of the pillars of modern physics. This theory can be applied to the study of the thermodynamic behavior of large systems of interacting particles, in which case it is referred to as equilibrium statistical...
    Resource Type:
    Dissertation
    Full Text:
    Radu Dascaliuc, Michael Rosulek, Enrique Thomann, and Ed Waymire for their time and dedication while

  • Mixing Times for Diffusive Lattice-Based Markov Chains

    Creator:
    Titus, Mathew W.
    Abstract:
    Markov chains have long been used to sample from probability distributions and simulate dynamical systems. In both cases we would like to know how long it takes for the chain's distribution to converge to within varepsilon of the stationary distribution in total variation distance; the answer to this is, called...
    Resource Type:
    Dissertation
    Full Text:
    , I would like to thank Dr. Thomann, Dr. Finch, Dr. Zhang, and Dr. Dascaliuc for agreeing to serve on