Mean first-passage time for random walks on generalized deterministic recursive trees

We describe a technique that allows the exact analytical computation of the mean first passage time (MFPT) for infinite families of trees using their recursive properties. The method is based in the relationship between the MFPT and the eigenvalues of the Laplacian matrix of the trees but avoids their explicit computation. We apply this technique to find the MFPT for a family of generalized deterministic recursive trees. The method, however, can be adapted to other self-similar tree families.

Figure 1

(Color online) The generalized deterministic recursive tree $T_{r,t}$ for $r=2$ and $t=0,1,2$.