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  • Arithmetic dynamical questions with local rationality conditions

    Creator:
    Noytaptim, Chatchai
    Abstract:
    We introduce a numerical criterion which allows us to bound the degree of any algebraic integer having all of Galois conjugates in an interval of length less than 4. Using this criterion, we study two arithmetic dynamical questions with local rationality conditions. First, we classify all unicritical polynomials defined over...
    Resource Type:
    Dissertation

  • An inner product on adelic measures

    Creator:
    Oberly, Peter J.
    Abstract:
    We define an inner product on a vector space of adelic measures over a number field $K$. We find that the norm induced by this inner product governs weak convergence at each place of $K$. The canonical adelic measure associated to a rational map is in this vector space, and...
    Resource Type:
    Dissertation
    Full Text:
    this dissertation. I wish to express sincere appreciation to Radu Dascaliuc, Thinh Nguyen, Thomas A

  • 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

  • Fourier Analysis and Equidistribution on the p-adic Integers

    Creator:
    Somasunderam, Naveen
    Abstract:
    In this dissertation, we use Fourier-analytic methods to study questions of equidistribution on the compact abelian group Zp of p-adic integers. In particu- lar, we prove a LeVeque-type Fourier analytic upper bound on the discrepancy of sequences. We establish p-adic analogues of the classical Dirichlet and Fejér kernels on R/Z,...
    Resource Type:
    Dissertation
    Full Text:
    mathematician. Learning real analysis with Dr. Radu Dascaliuc was such a thrilling experience. I cannot forget

  • 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