M2 PCS – Stochastic processes

Lectures for the master Physics of Complex Systems, S3

• monday 8h30-10h30 : Sorbonne Université, room 109, 24-14
• thursday 8h30-10h30 : Université Paris Cité, (1: Halle-471E, 2: Halle-470E, 3: Halle-165E, 4: Germain-1009, then Halle-470E)

Program:

1. Few concepts of probability
2. Introduction to Langevin equation
3. Markov processes and Master equation
4. Stochastic differential equations
5. Fokker-Planck equation
6. Functionals of stochastic processes

Lecture notes

• lecture notes (update: 11/12/2023)

Tutorials:

• Tut n°1 : Probability
• Tut n°2 : Probability (2)
• Tut n°3 : Langevin equation
• Tut n°4 : Master equation
• Tut n°5 : SDE (1)
• Tut n°6 : SDE (2) – Application for the Anderson localization in 1D
• Tut n°7 : FPE (1)
• Tut n°8 : FPE (2)
• Tut n°9 : FPE (3): first passage time
• Tut n°10 : Functionals

Exams:

• dec 2023 : exam & 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