Semi-analytical calculation showing the dependence of the PIM on dust turbulent diffusion, using the method in Sect. 3. Upper panel: ratio between the normalized PIM with dust turbulent diffusion (q_d,A) and that without (q_g,A), as a functionof the particles Stokes number. Both q_g,A and q_d,A are calculated using the analytical gap density profile of Duffell (2015). Lower panel: relative difference between the normalized PIM obtained with our semi-analytical calculation (q_d,a) and that obtained with our fitting formula (q_{d,A fit}, Eq. (11)).