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

Research output: Working paper

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.
Original languageEnglish
Publication statusUnpublished - 2011

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Stationary Measure
Sandpiles
Convergence Estimates
Dissipation
Random walk
Rate of Convergence
Sandpile Model
Zero
Spanning tree
Power Law
Coding
Upper bound
Converge
Estimate

Cite this

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title = "Rate of convergence estimates for the zero dissipation limit in Abelian sandpiles",
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.",
author = "Antal Jarai",
year = "2011",
language = "English",
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T1 - Rate of convergence estimates for the zero dissipation limit in Abelian sandpiles

AU - Jarai, Antal

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://arxiv.org/abs/1101.1437v2

M3 - Working paper

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

ER -