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We discuss various critical densities in sandpile models. The stationarydensity is the average expected height in the stationary state of afinite-volume model; the transition density is the critical point in theinfinite-volume counterpart. These two critical densities were generallyassumed to be equal, but this has turned out to be wrong for deterministicsandpile models. We show they are not equal in a quenched version of the Mannasandpile model either.  In the literature, when the transition density is simulated, it is implicitlyor explicitly assumed to be equal to either the so-called threshold density orthe so-called critical activity density. We properly define these auxiliarydensities, and prove that in certain cases, the threshold density is equal tothe transition density. We extend the definition of the critical activitydensity to infinite volume, and prove that in the standard infinite volumesandpile, it is equal to 1. Our results should bring some order in the preciserelations between the various densities.

Critical densities in sandpile models with quenched or annealed disorder