Spatial Persistence of Fluctuating Interfaces
Satya N. Majumdar, Alan J. Bray
Abstract
We show that the probability, P0(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 P0(l) l(-θ). Here θis a `spatial' persistence exponent, and takes different values, θs or θ0, depending on how the point from which l is measured is specified. While θs is related to fractional Brownian motion, and can be determined exactly, θ0 is non-trivial even for Gaussian interfaces.
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