Using the computer language of your choice, write a simulation of random walks in one dimension, on a
lattice of spacing delta x=1 and with discrete time steps, delta t=1. Each walker begins at the origin and at
each time step it takes a step to the right or left with equal probability, so that p_right=0.5, p_left=0.5.
of steps in each walk: 20
Number of walks: 10,000
You may structure your code as discussed in class, or come up with your own algorithm. Note, you will
need a random number generator.
Make the following graphs using your simulation data:
A. Mean square displacement vs. time, for time from t=0,1,2,3...20. Fit a straight line to the curve (by
eye is okay) and find the diffusion coefficient. Is it the same as predicted by theory?
B. Spatial distribution of walks at time = 20, normalized so the area under the curve is 1. [Note: after an
even number of steps, all walks end on evennumbered
C. For comparison, calculate the expected average spatial distribution at time T=20 and plot together
with your simulation data.