Einstein's Brownian Trajectories

Einstein realized that even if you can't model every particle in your system exactly, you can actually study the average behavior of all of your particles quite well. It's a random process, so on average, you're equally likely to go left in a time step as you are to go right. But as time progresses, you might get a series of left steps that take you a little bit further afield. So even though you don't go anywhere on average in this Brownian trajectory, you end up covering more ground.