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Spatial persistence and survival probabilities for fluctuating interfaces

M. Constantin·S. Das Sarma·C. Dasgupta
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Abstract

We report the results of numerical investigations of the steady-state (SS) and finite-initial-conditions (FIC) spatial persistence and survival probabilities for (1+1)--dimensional interfaces with dynamics governed by the nonlinear Kardar--Parisi--Zhang (KPZ) equation and the linear Edwards--Wilkinson (EW) equation with both white (uncorrelated) and colored (spatially correlated) noise. We study the effects of a finite sampling distance on the measured spatial persistence probability and show that both SS and FIC persistence probabilities exhibit simple scaling behavior as a function of the system size and the sampling distance. Analytical expressions for the exponents associated with the power-law decay of SS and FIC spatial persistence probabilities of the EW equation with power-law correlated noise are established and numerically verified.

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M. Constantin, S. Das Sarma, C. Dasgupta. 2004-05-14. Spatial persistence and survival probabilities for fluctuating interfaces. https://doi.org/10.1103/physreve.69.051603

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