Monte-Carlo Simulation
Klaus Werner
Introduction
Possible applications
Purpose of this lecture
Further reading
Uniform random numbers
Definition
Chaotic RN generator
Congruential generator
(
Exercise 1
)
Shift register generator
(
Exercise 2
)
A realistic RN generator
(
Exercise 3
) (
Exercise 4
) (
Exercise 5
)
Non-uniform random numbers
Definition
Inversion method
(
Exercise 1
) (
Exercise 2
)
Change of scale
(
Exercise 3
)
Rejection method
(
Exercise 4
)
Discrete distributions
(
Exercise 5
)
Superposition method
(
Exercise 6
)
Combining different methods
Combining random numbers
(
Exercise 7
)
The normal distribution
(
Exercise 8
)
One-dimensional random walk
Introduction
Diffusion equation
Solution of the diffusion equation
Solution via Monte Carlo
(
Exercise 1
)
Exact Solution
(
Exercise 2
)
Possibility of decay
(
Exercise 3
)
Drift and FP equation
(
Exercise 4
)
Time evolution
(
Exercise 5
)
Two-dimensional random walk
Diffusion equation
Solution of the diffusion equation
Solution via Monte Carlo
(
Exercise 1
)
Random direction
(
Exercise 2
)
Reflecting wall
(
Exercise 3
)