Random Walks Are Strange and Beautiful

Imagine, you find yourself blindfolded in the center of a dense, unknown city. At each crossroad, flips of a coin decide your next steps: left, right, forward, or backward. With no vision to guide you and randomness as your only companion, you start an unpredictable journey.

This, in essence, captures the spirit of random walks, a powerful concept from probability theory that is much more useful than walking through a city blindfolded with a coin in our hand. Physicists use random walks to describe the movement of particles, and have applications in areas ranging from biology to social sciences. Understanding random walks allows data scientists to model, simulate and predict stochastic processes from many different areas.

Moreover, in reinforcement learning, agents can perform random walks to explore their environments and gain information about the effects of their actions.

In short, random walks are extremely versatile. But that is a whole other story.

Applications aside, random walks are simply fascinating. Even without the math behind them, we can appreciate the beautiful, yet complex and puzzling world they open for us. If you randomly walk around the city long enough and trace your steps, your path reveals a…