  Observations of radio signals from distant pulsars provide a valuable tool
for investigation of interstellar turbulence. The time-shapes of the signals
are the result of pulse broadening by the fluctuating electron density in the
interstellar medium. While the scaling of the shapes with the signal frequency
is well understood, the observed anomalous scaling with respect to the pulsar
distance has remained a puzzle for more than 30 years. We propose a new model
for interstellar electron density fluctuations, which explains the observed
scaling relations. We suggest that these fluctuations obey Levy statistics
rather than Gaussian statistics, as assumed in previous treatments of
interstellar scintillations.
