In a one-dimensional random walk, a “walker” is confined to a long, narrow path and moves forward or backward in steps according to the results of repeatedly tossing a coin. The walker takes a step in one direction if the outcome is heads and in the opposite direction if the outcome is tails.
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For a walk along an infinite track, you can calculate a walker’s long-term behavior. The resulting trail wanders back and forth along the track, and the probability of the wanderer’s being a certain distance away from the starting point after taking a given number of steps is defined by the bell-shaped curve known as a Gaussian distribution.