# Rate of convergence estimates for the zero dissipation limit in Abelian sandpiles

### Reference:

Jarai, A., 2011. *Rate of convergence estimates for the zero dissipation limit in Abelian sandpiles.* Working Paper.

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### Abstract

We consider a continuous height version of the Abelian sandpile model with small amount of bulk dissipation gamma > 0 on each toppling, in dimensions d = 2, 3. In the limit gamma -> 0, we give a power law upper bound, based on coupling, on the rate at which the stationary measure converges to the discrete critical sandpile measure. The proofs are based on a coding of the stationary measure by weighted spanning trees, and an analysis of the latter via Wilson's algorithm. In the course of the proof, we prove an estimate on coupling a geometrically killed loop-erased random walk to an unkilled loop-erased random walk.

### Details

Item Type | Reports/Papers (Working Paper) | ||||

Creators | Jarai, A. | ||||

Related URLs |
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Departments | Faculty of Science > Mathematical Sciences | ||||

Status | Unpublished | ||||

ID Code | 28020 |

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