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arXiv · cond-mat/0009439

Spatial Persistence of Fluctuating Interfaces

Satya N. Majumdar·Alan J. Bray
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Abstract

We show that the probability, P_0(l), that the height of a fluctuating (d+1)-dimensional interface in its steady state stays above its initial value up to a distance l, along any linear cut in the d-dimensional space, decays as P_0(l) \sim l^(-θ). Here θis a `spatial' persistence exponent, and takes different values, θ_s or θ_0, depending on how the point from which l is measured is specified. While θ_s is related to fractional Brownian motion, and can be determined exactly, θ_0 is non-trivial even for Gaussian interfaces.

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Satya N. Majumdar, Alan J. Bray. 2000-10-25. Spatial Persistence of Fluctuating Interfaces. https://doi.org/10.1103/physrevlett.86.3700

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