Analytical results for generalized persistence properties of smooth processes

Abstract

We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the diffusion equation evolving from random initial conditions, one of the simplest coarsening systems. Exact results are obtained in certain limits, and rely on a new method to deal with constrained multiplicative processes. An excellent agreement of our analytical predictions with direct numerical simulations of the diffusion equation is found.

21 pages, 4 figures, to appear in Journal of Physics A

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Cited by in corpus (8)

• Large-Deviation Functions for Nonlinear Functionals of a Gaussian Stationary Markov Process
• Statistical Properties of Functionals of the Paths of a Particle Diffusing in a One-Dimensional Random Potential
• Persistence Exponents and the Statistics of Crossings and Occupation Times for Gaussian Stationary Processes
• Exact Occupation Time Distribution in a Non-Markovian Sequence and Its Relation to Spin Glass Models
• $A+A\to \varnothing$ model with a bias towards nearest neighbor
• Statistics of Multiple Sign Changes in a Discrete Non-Markovian Sequence
• Statistics of the occupation time for a random walk in the presence of a moving boundary
• Persistence and Life Time Distribution in Coarsening Phenomen