This course is divided into two parts:
- In the first part, we review important concepts about Markov chains: irreducibility, aperiodicity, recurrence, limiting and stationary distribution, the ergodic theorem, convergence speed towards equilibirum, spectral gap, cutoff phenomenon.
- In the second part, we apply these concept to sampling, and more precisely to Markov Chain Monte-Carlo (MCMC) sampling, exploring various applications (function minimization, coloring problem, Ising model). In the last part of the course, we also look at exact simulation.
- Professor: Olivier Lévêque
- Professor: Nicolas Macris
- Teacher: Anand Jerry George
- Teacher: Guanyu Zhang
