Abstract
The dynamics of linear stochastic growth equations on growing substratesis studied. The substrate is assumed to grow in time following the power lawtγ, where thegrowth index γ is an arbitrary positive number. Two different regimes are clearly identified: for smallγ the interface becomes correlated, and the dynamics is dominated by diffusion; for largeγ the interface stays uncorrelated, and the dynamics is dominated by dilution. In this secondregime, for short time intervals and spatial scales the critical exponents correspondingto the non-growing substrate situation are recovered. For long time differencesor large spatial scales the situation is different. Large spatial scales show theuncorrelated character of the growing interface. Long time intervals are studied bymeans of the auto-correlation and persistence exponents. It becomes apparent thatdilution is the mechanism by which correlations are propagated in this secondcase.
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