Now showing items 1-4 of 4

    • 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 ...
    • Eigenvalue fluctuations for random regular graphs 

      Johnson, Tobias Lee
      One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are <italic>universal</italic>. We probe the edges of universality by studying ...
    • Eigenvalue Fluctuations of Random Matrices beyond the Gaussian Universality Class 

      Paquette, Elliot (2013-11-14)
      The goal of this thesis is to develop one of the threads of what is known in random matrix theory as universality, which essentially is that a large class of matrices generalizing the Gaussian matrices (certain Wigner ...
    • 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 ...