4 research outputs found
Numerical Study of Local and Global Persistence in Directed Percolation
The local persistence probability P_l(t) that a site never becomes active up
to time t, and the global persistence probability P_g(t) that the deviation of
the global density from its mean value rho(t)- does not change its
sign up to time t are studied in a one-dimensional directed percolation process
by Monte Carlo simulations. At criticality, starting from random initial
conditions, both P_l(t) and P_g(t) decay algebraically with exponents theta_l ~
theta_g ~ 1.50(2), which is in contrast to previously known cases where theta_g
< theta_l. The exponents are found to be independent of the initial density and
the microscopic details of the dynamics, suggesting that theta_l and theta_g
are universal exponents. It is shown that in the special case of directed-bond
percolation, P_l(t) can be related to a certain return probability of a
directed percolation process with an active source (wet wall).Comment: revtex, 7 pages, including 6 eps figure