Lectures for the master Physics of Complex Systems, S3
- tuesday 8h30-12h45 : Université Paris Cité (Bâtiment Condorcet, room 050A)
- thursday 9h00-13h15 : Université Paris-Saclay (Bâtiment ℏ n°625, amphi A3)
- first lecture the tuesday 3rd september & last lecture the tuesday 15th october.
- exam: thursday 24th october 2024
Program:
- Few useful concepts of probability theory
- Introduction to Langevin equation
- Markov processes and Master equation
- Stochastic differential equations
- Fokker-Planck equation
- Functionals of stochastic processes
Lecture notes
- lecture notes (update 17/10/2024): here (refresh you browser)
Tutorials:
- Tut n°1 : Probability (1)
- Tut n°2 : Probability (2)
- Tut n°3 : Langevin equation
- Tut n°4 : Master equation (1)
- Tut n°5 : Master equation (2)
- Tut n°6 : SDE (1)
- Tut n°7 : SDE (2) – Application for the Anderson localization in 1D
- Tut n°8 : FPE (1)
- Tut n°9 : FPE (2)
- Tut n°10 : FPE (3) : first passage times
- Tut n°11 : Functionals
Exams:
- december 2023 : exam & correction
- october 2024 : exam: Linear drift — Conditioning in SDE & correction
Bibliography:
- C. W. Gardiner, Handbook of stochastic methods for physics, chemistry and the natural sciences, Springer, 1989
- H. Risken, The Fokker-Planck equation, Springer, 1989
- N. G. van Kampen, Stochastic processes in physics and chemistry, North-Holland, 1992