2001/11/12 by D. A. Head, David Head
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.65.027104
published as Phys. Rev. E 65, 027104 (2002) · 4 pages, 6 figures. To appear in Phys. Rev. E
arxiv created 2001/11/12 · openalex publication_date 2002/01/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The local persistence R(t), defined as the proportion of the system still in its initial state at time t, is measured for the Bak-Sneppen model. For one and two dimensions, it is found that the decay of R(t) depends on one of two classes of initial configuration. For a subcritical initial state, R(t)\ensuremath∼t^\ensuremath-\ensuremathθ, where the persistence exponent \ensuremathθ can be expressed in terms of a known universal exponent. Hence \ensuremathθ is universal. Conversely, starting from a supercritical state, R(t) decays by the anomalous form 1\ensuremath-R(t)\ensuremath∼t^\ensuremathτall until a finite time t0, where \ensuremathτall is also a known exponent. Finally, for the high dimensional model R(t) decays exponentially with a nonuniversal decay constant.