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The random growth of interfaces as a subordinated process

R. Failla·P. Grigolini·M. Ignaccolo·A. Schwettmann
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Abstract

We study the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, y(t)= h(t)-< h(t)>, which is depicted as being subordinated to a standard fluctuation-dissipation process with friction gamma. We argue that the main properties of Kardar-Parisi-Zhang theory, in one dimension, are derived by identifying the distribution of return times to y(0) = 0, which is a truncated inverse power law, with the distribution of subordination times. The agreement of the theoretical prediction with the numerical treatment of the 1 + 1 dimensional model of ballistic deposition is remarkably good, in spite of the finite size effects affecting this model.

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R. Failla, P. Grigolini, M. Ignaccolo, A. Schwettmann. 2004-07-06. The random growth of interfaces as a subordinated process. https://doi.org/10.1103/physreve.70.010101

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