Local persistence in directed percolation

We reconsider the problem of local persistence in directed site percolation. We present improved estimates of the exponent of persistence in all dimensions from 1+1 to 7+1, obtained using new algorithms and using improved implementations of existing ones. We verify the strong corrections to scaling for 2+1 and 3+1 dimensions found in previous analyses, but we show that scaling is much better satisfied for very large and very small dimensions. For d>4 (d is the spatial dimension), the persistence exponent depends non-trivially on d, in qualitative agreement with the non-universal values calculated recently by Fuchs et al (2008 J. Stat. Mech. P04015). These results are mainly based on efficient simulations of clusters evolving under the time reversed dynamics with a permanently active site and a particular survival condition discussed by Fuchs et al. These simulations suggest also a new critical exponent ζ which describes the growth of these clusters conditioned on survival, and which turns out to be the same as the exponent, η+δ in standard notation, of surviving clusters under the standard DP evolution