Transition behavior on lattices with ladders

We consider a d=2-dimensional, planar lattice of coordination number v=4 separated into distinct regions by a two/three-leg ladder. Random walks on this composite inhomogeneous lattice are studied as a function of the coupling of the ladder to the host lattice and with respect to the location of the trapping site. We find that the efficiency of trapping at sites on the host lattice decreases, whereas the efficiency of trapping at ladder sites increases, both dramatically, as the coupling of the ladder to the lattice decreases.