Simulation of Random Walk

Random walk model is made to explain the Brownian motion.

In this simulation, we assume that there's a group of drunkards walking from same area at the same time. Then we can make the following hypothesis. The walking speed is same and they cannot affect each other. The distance of a step they walk is distributed uniformly in a certain range. After some walks, it is obvious that there will be a distribution for the number of drunkards on the plain. What we do is to display the probability density function by simulation. It can be proved that the distribution is subject to the Weibull distribution.The function is,
f=6r*exp(-3*r^2/(na^2))/(na^2)
f —— describes the probability density of the drunkards at distance r
n —— describes the number of steps they have walked
a —— describes the range of a drunkard walked each time

We can see from the simulation that the theoretical function is quite similar with the experimental function, showing the correctness of this model. If you want to know the theoretical model of this simulation, contact the author by email.