Persistence with Partial Survival

Details Persistence with Partial Survival Persistence with Partial Survival

1998-05-28

arxiv.org/abs/cond-mat/9805380v2

Phys. Rev. Lett. 81, 2626 (1998)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 2 figures, references added, to appear in Phys.Rev.Lett

Scientific paper

10.1103/PhysRevLett.81.2626

We introduce a parameter $p$, called partial survival, in the persistence of stochastic processes and show that for smooth processes the persistence exponent $\theta(p)$ changes continuously with $p$, $\theta(0)$ being the usual persistence exponent. We compute $\theta(p)$ exactly for a one-dimensional deterministic coarsening model, and approximately for the diffusion equation. Finally we develop an exact, systematic series expansion for $\theta(p)$, in powers of $\epsilon=1-p$, for a general Gaussian process with finite density of zero crossings.

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