  The fraction r(t) of spins which have never flipped up to time t is studied
within a linear diffusion approximation to phase ordering. Numerical
simulations show that, even in this simple context, r(t) decays with time like
a power-law with a non-trival exponent $\theta$ which depends on the space
dimension. The local dynamics at a given point is a special case of a
stationary gaussian process of known correlation function and the exponent
$\theta$ is shown to be determined by the asymptotic behavior of the
probability distribution of intervals between consecutive zero-crossings of
this process. An approximate way of computing this distribution is proposed, by
taking the lengths of the intervals between successive zero-crossings as
independent random variables. The approximation gives values of the exponent
$\theta$ in close agreement with the results of simulations.
