Spatial persistence of fluctuating interfaces.
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) approximately l(theta). Here straight theta is a "spatial" persistence exponent, and takes different values, straight theta(s) or straight theta(0), depending on how the point from which l is measured is specified. These exponents are shown to map onto corresponding temporal persistence exponents for a generalized d = 1 random-walk equation. The exponent straight theta(0) is nontrivial even for Gaussian interfaces.
Majumdar
S N
SN
Laboratoire de Physique Quantique (UMR C5626 du CNRS), Université Paul Sabatier, 31062 Toulouse Cedex, France.
Bray
A J
AJ