Project Title: Mixing Times of Markov Chains

Faculty Sponsor: Cameron McLeman

Department: Mathematics

Telephone: 810.237.6689

E-Mail: mclemanc@umflint.edu

Project Description: The goal of this project will be to further existing research on the mixing times of Markov chains run on toroidal lattices or similar structures.  This will be done predominantly by a combination of the analysis of the eigenvalues of the corresponding adjacency matrix, and by using the technique of path coupling to bound various stationary time metric

Student Tasks & Responsibilities: 

  • Use SAGE programming system to calculate and organize data about eigenvalues of adjacency matrices of graphs.
  • Experiment with various couplings of Markov chains in an attempt to find an optimal one.
  • Use LaTeX to keep track of progress and write up results.

Minimum Student Qualifications: Fluency in SAGE and LaTeX, strong background in Markov chains and linear algebra.  Knowledge of Pade approximations preferable.