Infinite volume limit of the Abelian sandpile model in dimensions d ≥ 3
We study the Abelian sandpile model on . In d ≥ 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit μ of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure μ , and...
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| Veröffentlicht in: | Probability theory and related fields 2008-05, Vol.141 (1-2), p.181-212 |
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| container_title | Probability theory and related fields |
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| creator | Járai, Antal A. Redig, Frank |
| description | We study the Abelian sandpile model on
. In
d
≥ 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit
μ
of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure
μ
, and study ergodic properties of this process. The main techniques we use are a connection between the statistics of waves and uniform two-component spanning trees and results on the uniform spanning forest measure on
. |
| doi_str_mv | 10.1007/s00440-007-0083-0 |
| format | Article |
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. In
d
≥ 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit
μ
of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure
μ
, and study ergodic properties of this process. The main techniques we use are a connection between the statistics of waves and uniform two-component spanning trees and results on the uniform spanning forest measure on
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. In
d
≥ 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit
μ
of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure
μ
, and study ergodic properties of this process. The main techniques we use are a connection between the statistics of waves and uniform two-component spanning trees and results on the uniform spanning forest measure on
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. In
d
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μ
of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure
μ
, and study ergodic properties of this process. The main techniques we use are a connection between the statistics of waves and uniform two-component spanning trees and results on the uniform spanning forest measure on
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| ispartof | Probability theory and related fields, 2008-05, Vol.141 (1-2), p.181-212 |
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| source | SpringerNature Journals; EBSCOhost Business Source Complete |
| subjects | Avalanches Economics Exact sciences and technology Finance General topics Graph theory Inference from stochastic processes time series analysis Insurance Management Markov analysis Markov processes Mathematical and Computational Biology Mathematical and Computational Physics Mathematics Mathematics and Statistics Operations Research/Decision Theory Probability Probability and statistics Probability Theory and Stochastic Processes Quantitative Finance Random walk theory Sciences and techniques of general use Statistics Statistics for Business Stochastic processes Studies Theoretical |
| title | Infinite volume limit of the Abelian sandpile model in dimensions d ≥ 3 |
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