2005/09/30 by Satya N. Majumdar, Chandan Dasgupta · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Applied mathematics #Brownian motion #Complex Systems and Time Series Analysis #Discretization #Geometry #Mathematical analysis #Mathematics #Physics #Probability distribution #Scaling #Statistical physics #Statistics #Steady state (chemistry) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.73.011602
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
arxiv created 2005/12/19 · openalex publication_date 2006/01/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.