Active width at a slanted active boundary in directed percolation

The width W of the active region around an active moving wall in a directed percolation process diverges at the percolation threshold $p_c$ as $W\simeq A{\epsilon }^{-{\nu }_{\Vert }}\ln ({\epsilon }_0/\epsilon ),$ with $\epsilon {=p}_c-p,$ ${\epsilon }_0$ a constant, and ${\nu }_{\Vert }=1.734\mathrm{}$ the critical exponent of the characteristic time needed to reach the stationary state ${\xi }_{\Vert }\sim {\epsilon }^{-{\nu }_{\Vert }}.$ The logarithmic factor arises from screening the statistically independent needle shaped subclusters in the active region. Numerical data confirm this scaling behavior.