Now showing items 1-8 of 8

    • Aspects of Markov Chains and Particle Systems 

      Ganguly, Shirshendu
      The thesis concerns asymptotic behavior of particle systems and the underlying Markov chains used to model various natural phenomena. The objective is to describe and analyze stochastic models involving spatial structure ...
    • A Geometric Perspective on First-Passage Competition 

      Blair-Stahn, Nathaniel Deveroux (2013-04-17)
      We study the macroscopic geometry of first-passage competition on the integer lattice <bold>Z</bold><super>d</super>, with a particular interest in describing the behavior when one species initially occupies the exterior ...
    • Markov chain mixting time, card shuffling and spin systems dynamics 

      Ning, Weiyang (2013-07-25)
      The mixing time of a Markov chain describes how fast the Markov chain converges to its stationary distribution. In this thesis, we survey some of the knowledge and main tools available in this field by looking at examples. ...
    • Novel uses of the Mallows model in coloring and matching 

      Levy, Avi William
      A natural model of a highly ordered random ranking is the Mallows model. Disorder is measured by the number of inversions; these are pairs of elements whose order is reversed. The Mallows model assigns to each ranking of ...
    • Random Permutations and Simplicial Complexes 

      Fowler, Christopher F
      We study the asymptotic behavior of distributions on two different combinatorial objects, permutations and simplicial complexes. First we study strong α-logarithmic measures on the symmetric group, including the well- ...
    • Random recursion 

      Junge, Matthew S.
      We study the limiting behavior of three stochastic processes. Two are interacting particle systems, the frog model and coalescing random walk. We work out transience and recurrence properties on various graphs. The last ...
    • Spectral analysis in bipartite biregular graphs and community detection 

      Brito, Gerandy
      This thesis concerns to spectral gap of random regular graphs and consists of two main con- tributions. First, we prove that almost all bipartite biregular graphs are almost Ramanujan by providing a tight upper bound for ...
    • Three Problems in Discrete Probability 

      Slivken, Erik Dustin
      In this thesis we present three problems. The first problem is to find a good description of the number of fixed points of a 231-avoiding permutation. We use a bijection from Dyck paths to 231-avoiding permutations that ...