Introduction to dynamical large deviations of Markov processes by Hugo Touchette in 2018
Video lectures
I. Introduction
II. Markov processes
A. Stochastic differential equations
B. State distribution and generator
C. Examples
- Kramers or underdamped Langevin equation
- Overdamped Langevin equation
- Ornstein-Uhlenbeck process
D. Equilibrium versus nonequilibrium processes
E. Comparison with quantum mechanics
F. Further reading
III. Dynamical observables
IV. Large deviations
A. Large deviation principle
B. Spectral problem
C. Symmetrization
D. Example: Ornstein-Uhlenbeck process
E. Further reading
Appendix A: Dual spaces for Markov processes
Appendix B: Non-Hermitian operators