After successful completion of the course, students are able to...
...describe and analyze random walks on graphs
...describe the relationship between the geometry of the graph and the long term behavior of the random walk, in particular
...characterize recurrence and transience in terms of the electrical properties of the graph
...investigate questions of convergence towards the stationary distribution (mixing times, spectral gap) for finite-state Markov chains
Random walks and electric networks
Random walks on finite graphs: speed of convergence
Lecture and homework problems
Exam
Basics of probability theory and stochastic processes, Markov Chain, Gaussian processes