  We discuss various critical densities in sandpile models. The stationary
density is the average expected height in the stationary state of a
finite-volume model; the transition density is the critical point in the
infinite-volume counterpart. These two critical densities were generally
assumed to be equal, but this has turned out to be wrong for deterministic
sandpile models. We show they are not equal in a quenched version of the Manna
sandpile model either.
  In the literature, when the transition density is simulated, it is implicitly
or explicitly assumed to be equal to either the so-called threshold density or
the so-called critical activity density. We properly define these auxiliary
densities, and prove that in certain cases, the threshold density is equal to
the transition density. We extend the definition of the critical activity
density to infinite volume, and prove that in the standard infinite volume
sandpile, it is equal to 1. Our results should bring some order in the precise
relations between the various densities.
