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Fluctuations of a Surface Submitted to a Random Average Process

1998
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Electronic Journal of Probability
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We consider a hypersurface of dimension d imbedded in a d + 1 dimensional space. For each x ∈ Z d , let η t (x) ∈ R be the height of the surface at site x at time t. At rate 1 the x-th height is updated to a random convex combination of the heights of the 'neighbors' of x. The distribution of the convex combination is translation invariant and does not depend on the heights. This motion, named the random average process (RAP), is one of the linear processes introduced by Liggett (1985). Special

doi:10.1214/ejp.v3-28
fatcat:4lqoxwv3hjgyrfcvrijiehcyde