Spatial survival probability for one-dimensional fluctuating interfaces in the steady state

Abstract

We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from analysis of steady-state profiles generated by integrating a spatially discretized form of the Edwards-Wilkinson equation to long times. We show that the survival probability exhibits scaling behavior in its dependence on the system size and the `sampling interval' used in the measurement for both `steady-state' and `finite' initial conditions. Analytic results for the scaling functions are obtained from a path-integral treatment of a formulation of the problem in terms of one-dimensional Brownian motion. A `deterministic approximation' is used to obtain closed-form expressions for survival probabilities from the formally exact analytic treatment. The resulting approximate analytic results provide a fairly good description of the numerical data.

RevTeX4, 21 pages, 8 .eps figures, changes in sections IIIB and IIIC and in Figs 7 and 8, version to be published in Physical Review E

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• Generating discrete-time constrained random walks and Lévy flights
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• Crossing intervals of non-Markovian Gaussian processes
• Generating stochastic trajectories with global dynamical constraints
• Maximum relative height of one-dimensional interfaces : from Rayleigh to Airy distribution
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• Distribution of zeros in the rough geometry of fluctuating interfaces
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