http://www.ck12.org Chapter 31. Random Walks 1
31.1 Introduction
This chapter provides an introduction to the random walk, a model widely used in physics and other fields. It explains
the theory behind the basics of one-dimensional random walks, and the next chapter then shows how to model them
in Python — an open source programing language widely used within the scientific community.
Much of modern physics relies on computer simulations for results, yet this field is largely left out of high school
physics classrooms. It is the goal of this chapter to bridge this gap by providing instructions for running simple
models side by side with the theory they mirror. In this sense, the chapter is both an overview of random walks and
a short introduction to computational programing.
One-Dimensional Random Walks
This type of random walk is conceptually a very simple model. Imagine starting at a point on a line, and then taking
a step either to the left or to the right every couple of seconds. This is a typical example of a one-dimensional random
walk. Which direction you pick, how big of a step you take, and how often you take steps are all parameters that can
differentiate different random walks, but they all have these common basic features.
The ’random’ in the title of this chapter refers to the fact that you will pick the direction of your steps randomly.
Since the simplest practical idea of randomness that we have is a two-sided coin, we interpret our random walk in
terms of that model. Specifically, each time a coin is flipped, the person flipping it takes a step — to the right if it
lands on heads, and to the left if it lands on tails:
Notice that the coin doesn’t have to be fair: we simply said that there isPprobability of it landing on tails, and
therefore 1−Pprobability of it landing on heads. This probability is one of theparametersmentioned above.
Here’s a list of important ones for this type of random walk:
One-dimensional Random Walk Parameters- Probability of picking left/right (P).