Project 6: Random Walk
What’s a random walk?
In 1827, the Scottish botanist Robert Brown observed that pollen particles suspended in water seemed to float around at random. He had no plausible explanation for what came to be known as Brownian motion, and made no attempt to model it mathematically. Louis Bachelier presented a clear mathematical model in his doctoral thesis, The Theory of Speculation in 1900. His thesis was largely ignored by respectable academics because it dealt with the then disreputable field of understanding financial markets. In 1905, Albert Einstein used similar stochastic thinking in physics to describe how it could be used to confirm the existence of atoms. People seemed to think that understanding physics was more important than making money, and the world started paying attention.
Brownian motion is an example of a random walk. Today, random walks are widely used to model physical processes like diffusion, biological processes like the kinetics of displacement of RNA from heteroduplexes by DNA, and social processes like movements of the stock market.
We are interested in random walks because of their wide applications to many problems, and for learning more about how to structure simulations nicely in Python.