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.
Analytical results for generalized persistence properties of smooth processes
Baldassarri A;
2000
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.File in questo prodotto:
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