Diffusive persistence and the "sign-time" distribution

T. J. Newman, Z. Toroczkai

    Research output: Contribution to journalArticlepeer-review

    25 Citations (Scopus)


    We present a method for extracting the persistence exponent ? for the diffusion equation, based on the distribution P of "sign times." With the aid of a numerically verified ansatz for P, we derive an analytic formula for ? (in arbitrary spatial dimension d) which we conjecture to be the exact result. Our results are in excellent agreement with previous numerical studies. Furthermore, our results indicate a qualitative change in P above d = 36, signaling the existence of a sharp change in the ergodic properties of the diffusion field.
    Original languageEnglish
    Pages (from-to)R2685-R2688
    Number of pages4
    JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
    Issue number3
    Publication statusPublished - 1 Sept 1998


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