  We present a new method for extracting the persistence exponent theta for the
diffusion equation, based on the distribution P of `sign-times'. With the aid
of a numerically verified Ansatz for P we derive an exact formula for theta in
arbitrary spatial dimension d. Our results are in excellent agreement with
previous numerical studies. Furthermore, our results indicate a qualitative
change in P above d ~ 36, signalling the existence of a sharp change in the
ergodic properties of the diffusion field.
