What it shows:
A random walk is a mathematical model for the movement of a particle that is under the influence of some random or stochastic mechanism that affects its direction of movement. Physical situations that can be described by random walks include diffusion and Brownian motion.
How it works:
The board is a two dimensional random walk model consisting of a hexagonal array of corks, 1 11 to a side (331 corks in all), with each point of the hexagon given a number. The random walk begins from the center cork and the roll of a die determines which direction the particle moves (in a real random walk, any angle is possible; here we are limited to six directions). The path length is the distance between corks, and at each cork the die is cast again. The cork 'selected' is removed so that the particle's path is revealed as a corkless trail. This trail is visible because the board is a light box; behind the array is a fluorescent lamp.
figure 1. the random walk board
Nice and clear, but a bit dry. Slightly more fun could be passing a beach ball around the audience with the roll of a die again determining its direction of motion.
Many mathematics texts will hit you with all the formalism. A good example is:
P. Révész Random Walk in Random and Non-Random Environments (World Scientific Publishing 1990)
1 #7 corks in 2cm holes.