Uniform threshold for fixation of the stochastic sandpile model on the line
13 Jan 2020
•
Podder Moumanti
•
Rolla Leonardo T.
We consider the abelian stochastic sandpile model. In this model, a site is
deemed unstable when it contains more than one particle...Each unstable site,
independently, is toppled at rate $1$, sending two of its particles to
neighbouring sites chosen independently. We show that when the initial average
density is less than $1/2$, the system locally fixates almost surely. We
achieve this bound by analysing the parity of the total number of times each
site is visited by a large number of particles under the sandpile dynamics.(read more)