Conformal covariance of the Abelian sandpile height one field

Maximilian Dürre

Stochastic Processes and their Applications, 2009, vol. 119, issue 9, 2725-2743

Abstract: We study the scaling limit for the height one field of the two-dimensional Abelian sandpile model. The scaling limit for the covariance having height one at two macroscopically distant sites, more generally the centred height one joint moment of a finite number of macroscopically distant sites, is identified and shown to be conformally covariant. The result is based on a representation of the height one joint intensities that is close to a block-determinantal structure.

Keywords: Abelian; sandpile; model; Scaling; limit; Determinantal; process; Conformal; covariance (search for similar items in EconPapers)
Date: 2009
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