  The time and size distribution of the waves of topplings in the Abelian
sandpile model are expressed as the first arrival at the origin distribution
for a scale invariant, time inhomogeneous Fokker-Planck equation. Assuming a
linear conjecture for the the time inhomogeneity exponent as function of loop
erased random walk (LERW) critical exponent, suggested by numerical results,
this approach allows to estimate the lower critical dimension of the model and
the exact value of the critical exponent for LERW in three dimension. The
avalanche size distribution in two dimensions is found to be the difference
between two closed power laws.
