Beyond Brownian Motion

FEB 01, 1996

Fractal generalizations of Brownian motion have proven to be a rich field in probability theory, statistical physics and chaotic dynamics.

DOI: 10.1063/1.881487

Joseph Klafter

Michael F. Shlesinger

Gert Zumofen

Newtonian physics began with an attempt to make precise predictions about natural phenomena, predictions that could be accurately checked by observation and experiment. The goal was to understand nature as a deterministic, “clockwork” universe. The application of probability distributions to physics developed much more slowly. Early uses of probability arguments focused on distributions with well‐defined means and variances. The prime example was the Gaussian law of errors, in which the mean traditionally represented the most probable value from a series of repeated measurements of a fixed quantity, and the variance was related to the uncertainty of those measurements.

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More about the authors

Joseph Klafter, Tel Aviv University, Israel.

Michael F. Shlesinger, Office of Naval Research, Arlington, Virginia.

Gert Zumofen, Laboratory for Physical Chemistry of the Eidgenössische Technische Hochschule, Zurich, Switzerland.