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Analytical results for generalized persistence properties of smooth processes

Ivan Dornic·Anaël Lemaître·Andrea Baldassarri·Hugues Chaté
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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.

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Ivan Dornic, Anaël Lemaître, Andrea Baldassarri, Hugues Chaté. 2000-09-07. Analytical results for generalized persistence properties of smooth processes. https://doi.org/10.1088/0305-4470%2F33%2F42%2F303

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