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"Physics in the Noise," by Michael F. Shlesinger. Nature, 7 June 2001.
Shlesinger traces the development of work in random walks, from Einstein's and Jean Perrin's observations on motion to Lord Rayleigh's connection between diffusive heat flow and random scattering, to Scher's and Montroll's experiments with charged pairs of electrons and holes. Of note are new developments based on the work of Paul Levy in the 1920s. "These non-gaussian 'Levy flights' do not possess the smooth flow of a diffusion process. Because of the likelihood of longer and longer jumps, the flight paths burst out from their origin, hitting a fractal clustered set of points. But how could such mathematical conjuring ever find a physical application? Levy's work stayed in the mathematical literature, unknown in physics until recently ... It was a big surprise that random Levy walks appeared in dynamical systems that are deterministic without a hint of probability in the equations of motion. The key is that seemingly random-like behaviour can arise through nonlinearity."
--- Annette Emerson
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