A Random Walk: Stumbling across Connections

  • A Random Walk: Stumbling across Connections

    Nicholas H. Wasserman
    Ideas in statistics, probability, stochastic processes, and algebra follow the steps of a wandering professor.
    A random walk, also colloquially known as a drunkard’s walk, was a term first introduced by Karl Pearson in 1905 (Pearson 1905). Random walks are paths that consist of a succession of random steps. Despite the seemingly unknown nature of events of chance, it is the random and recursive nature of these walks that permit more precise study and results to be obtained, drawing on probability computations. Although random walks perhaps unrealistically simplify real-life situations, they are particularly powerful because many real-world phenomena can be modeled sufficiently well by them—for example, a molecule bumping around as it travels through a gas, the price of a fluctuating stock, or a random person’s path around city blocks.
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