Electronic Communications in Probability

Symmetric exclusion as a model of non-elliptic dynamical random conductances

Luca Avena

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We consider a finite range symmetric exclusion process on the integer lattice in any dimension. We interpret it as a non-elliptic time-dependent random conductance model by setting conductances equal to one over the edges with end points occupied by particles of the exclusion process and to zero elsewhere. We prove a law of large number and a central limit theorem for the random walk driven by such a dynamical field of conductances using the Kipnis-Varhadan martingale approximation. Unlike the tagged particle in the exclusion process, which is in some sense similar to this model, this random walk is diffusive even in the one-dimensional nearest-neighbor symmetric case.

Article information

Electron. Commun. Probab., Volume 17 (2012), paper no. 44, 8 pp.

Accepted: 1 October 2012
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments
Secondary: 82C22: Interacting particle systems [See also 60K35]

Random conductances law of large numbers invariance principle exclusion process

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Avena, Luca. Symmetric exclusion as a model of non-elliptic dynamical random conductances. Electron. Commun. Probab. 17 (2012), paper no. 44, 8 pp. doi:10.1214/ECP.v17-2081. https://projecteuclid.org/euclid.ecp/1465263177

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