Contents of the lecture

Simulations of intrinsically stochastic processes

Random walks; properties; Monte Carlo simulation of 1D and 2D RWs. RW to simulate diffusion processes:

- 1D Random walks: introduction; analytical properties; diffusion equation; continuum limit

- Numerical simulation of Random walks

- 2D Random walks: different algorithms

- Something on modified random walks (restricted RW; self-avoiding walks; persistent RW; ...)
 

Some references:

- Some  lectures on Random Walk Simulation by R. Landau

- Chapter 6 "Deterministic Randomness" and 7 "Monte-Carlo Techniques" of "Computational Physics" by Landau-Paez (1st ed., 1997)

- Chapter 7 (Random Processes) and 12 (Random Walks) of  "Computer simulation Methods: application to Physical Systems", by H. Gould and J. Tobochnik, Addison Wesley (2st edition 1995), on the Web

- See "A Survey of Computational Physics: Introductory Computational Science" by Rubin H. Landau, Manuel Jose Paez and Cristian C. Bordeianu (2008), Princeton University Press, or the older "Computational Physics" by Landau and Paez (1997)