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) - [rho(t)] does not change its sign up to time t are studied in a (1+1)-dimensional directed percolation process by Monte-Carlo simulations. At criticality, starting from random initial conditions, P-l(t) decays algebraically with the exponent theta(l) approximate to 1.50(2). The value is found to be independent of the initial density and the microscopic details of the dynamics, suggesting theta(l) is an universal exponent. The global persistence exponent theta(g) is found to be equal or larger than theta(l). This contrasts with previously known cases where theta(g) < theta(l). 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).