Analytical results for generalized persistence properties of smooth processes

Details Analytical results for generalized persistence properties of smooth processes Analytical results for generalized persistence properties of smooth processes

2000-09-07

arxiv.org/abs/cond-mat/0009109v1

J. Phys. A 33 (2000), pp. 7499-7513

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/0305-4470/33/42/303

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.

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