PPT Slide
Suggested further “research”
1. Prove (by computer simulations or analytically if you can…) that 3d is the lowest dimensional space where somebody can get completely lost...
I.e. the probability that the r.w. track crosses the starting point is going to zero, when the number of steps is going to infinity….
What will happen in 1d and 2d?
(use square and cubic lattice sites in 2d and 3d, respectively)
2. Study by computer simulations the self-avoiding random walk. The self-avoiding random walk is a random walk, where the walker cannot move on a site previously visited.
What will one expect in this case for the ? coefficient in 1d, 2d and 3d?
3. Study by computer simulations the ? coefficient of a 2d Levy-flight. The Levy flight is a random walk consisting of random jumps. The probability of jumping to a site at distance s, from the original site is decreasing as a power low with s and does not depend on the chosen direction.