On infinite bounded-degree graphs, divisible sandpiles with i.i.d. initial masses of mean μ stabilize almost surely if μ < 1 and masses have finite p-moment for p > 3, but explode if μ ≥ 1; the conditions are nearly sharp via counterexamples on other graphs.
Convergence of the random A belian sandpile
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
citation-role summary
method 1
citation-polarity summary
fields
math.PR 1years
2026 1verdicts
UNVERDICTED 1roles
method 1polarities
use method 1representative citing papers
citing papers explorer
-
Divisible sandpiles via random walks in random scenery
On infinite bounded-degree graphs, divisible sandpiles with i.i.d. initial masses of mean μ stabilize almost surely if μ < 1 and masses have finite p-moment for p > 3, but explode if μ ≥ 1; the conditions are nearly sharp via counterexamples on other graphs.