  1/f noise, the major source of dephasing in Josephson qubits, may be produced
by an ensemble of two-level systems. Depending on the statistical properties of
their distribution, the noise distribution can be Gaussian or non-Gaussian. The
latter situation is realized, for instance, when the distribution of coupling
strengths has a slowly decaying power-law tail. In this regime questions of
self-averaging and sample-to-sample fluctuations become crucial. We study the
dephasing process for a class of distribution functions and analyze the
self-averaging properties of the results.
