Modern Theory of Markov Chains

Project Topic Suggestions

• Coin-tossing games
• Stochastic inequalities
• Using Gibbs samplers in mathematical proofs (e.g., Holley's theorem)
• Moran model of natural selection
• Bernoulli-Laplace model of diffusion
• Symmetry-breaking in infinite Markov chains
• Mixing times from set hitting times
• Markov random fields
• Markov chains as dynamical systems
• Zero-one laws for Markov chains
• Monte Carlo for approximate counting
• Monte Carlo for cracking substitution encryption
• Mixing time of the Gibbs sampler for the Ising model (hard-core model, etc.)
• Efficient Monte Carlo algorithms for sampling from the Ising model (hard-core model, etc.)
• Monte Carlo sampling of domino tilings of the square lattice (or diamond tilings of the triangular lattice)
• Monte Carlo simulation of the hard disk model
• Perfect sampling (Propp-Wilson method)
• An uncovered chapter from the book
• ...