Analytical results for generalized persistence properties of smooth processes
Statistical Mechanics
2009-10-31 v1
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.
Cite
@article{arxiv.cond-mat/0009109,
title = {Analytical results for generalized persistence properties of smooth processes},
author = {Ivan Dornic and Anaël Lemaître and Andrea Baldassarri and Hugues Chaté},
journal= {arXiv preprint arXiv:cond-mat/0009109},
year = {2009}
}
Comments
21 pages, 4 figures, to appear in Journal of Physics A