Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"Physics in the Noise," by Michael F. Shlesinger. Nature, 7 June 2001.

Shlesinger traces the development of work in random walks, from Einstein's andJean Perrin's observations on motion to Lord Rayleigh's connection betweendiffusive heat flow and random scattering, to Scher's and Montroll'sexperiments with charged pairs of electrons and holes. Of note are newdevelopments 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. Becauseof the likelihood of longer and longer jumps, the flight paths burst out fromtheir origin, hitting a fractal clustered set of points. But how could suchmathematical conjuring ever find a physical application? Levy's work stayed inthe mathematical literature, unknown in physics until recently ... It was a bigsurprise that random Levy walks appeared in dynamical systems that aredeterministic without a hint of probability in the equations of motion. The keyis that seemingly random-like behaviour can arise through nonlinearity."

--- Annette Emerson