  An isotropic passive scalar field $T$ advected by a rapidly-varying velocity
field is studied. The tail of the probability distribution $P(\theta,r)$ for
the difference $\theta$ in $T$ across an inertial-range distance $r$ is found
to be Gaussian. Scaling exponents of moments of $\theta$ increase as $\sqrt{n}$
or faster at large order $n$, if a mean dissipation conditioned on $\theta$ is
a nondecreasing function of $|\theta|$. The $P(\theta,r)$ computed numerically
under the so-called linear ansatz is found to be realizable. Some classes of
gentle modifications of the linear ansatz are not realizable.
