  We introduce a natural stochastic extension, called SSP, of the abelian
sandpile model(ASM), which shares many mathematical properties with ASM, yet
radically differs in its physical behavior, for example in terms of the shape
of the steady state and of the avalanche size distribution. We establish a
basic theory of SSP analogous to that of ASM, and present a brief numerical
study of its behavior. Our original motivation for studying SSP stems from its
connection to the LLL algorithm established in another work by the authors [5].
The importance of understanding how LLL works cannot be stressed more,
especially from the point of view of lattice-based cryptography. We believe SSP
serves as a tractable toy model of LLL that would help further our
understanding of it.
