  A new model for stock price fluctuations is proposed, based upon an analogy
with the motion of tracers in Gaussian random fields, as used in turbulent
dispersion models and in studies of transport in dynamically disordered media.
Analytical and numerical results for this model in a special limiting case of a
single-scale field show characteristics similar to those found in empirical
studies of stock market data. Specifically, short-term returns have a
non-Gaussian distribution, with super-diffusive volatility, and a fast-decaying
correlation function. The correlation function of the absolute value of returns
decays as a power-law, and the returns distribution converges towards Gaussian
over long times. Some important characteristics of empirical data are not,
however, reproduced by the model, notably the scaling of tails of the
cumulative distribution function of returns.
