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Universal persistence exponents in an extremally driven system
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 1 and
2 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)\sim
t^{-\theta}, where the persistence exponent \theta can be expressed in terms of
a known universal exponent. Hence \theta is universal. Conversely, starting
from a supercritical state, R(t) decays by the anomalous form 1-R(t)\sim
t^{\tau_{\rm ALL}} until a finite time t_{0}, where \tau_{\rm ALL} is also a
known exponent. Finally, for the high dimensional model R(t) decays
exponentially with a non--universal decay constant.Comment: 4 pages, 6 figures. To appear in Phys. Rev.