Random walk increasing distance
It's easiest to understand with a one-dimensional random walk.  After $n$ steps, the typical value for the distance from the origin is proportional to $\sqrt{n}$.  Thus, the more steps you take, the greater the typical distance from the origin.  For an analysis and explanation, see https://en.wikipedia.org/wiki/Random_walk#One-dimensional_random_walk.  The math is well-developed in many standard places, so I'm not going to repeat it here.