Wonderful article, going from random walk to a Gaussian distribution. As an aside, I feel that normal distribution is way overused in practical contexts (apart from explaining Brownian motion, heights of people, and some other interesting observations). Heavy-tailed distributions that follow pareto or power-law, tend to be closer to actual reality, on many phenomena.
Obviously use the appropriate distribution for your problem. But the Gaussian is used a lot for very good reasons, the central limit theorem being a particularly strong one.
