  We introduce a formalism based on a continuous time approximation, to study
the characteristics of Page Rank random walks. We find that the diffusion of
the occupancy probability has a dynamics that exponentially "forgets" the
initial conditions and settles to a steady state that depends only on the
characteristics of the network. In the special case in which the walk begins
from a single node, we find that the largest eigenvalue of the transition value
(lambda=1) does not contribute to the dynamic and that the probability is
constant in the direction of the corresponding eigenvector. We study the
process of visiting new node, which we find to have a dynamic similar to that
of the occupancy probability. Finally, we determine the average transit time
between nodes <T>, which we find to exhibit certain connection with the
corresponding time for Levy walks. The relevance of these results reside in
that Page Rank, which are a more reasonable model for the searching behavior of
individuals, can be shown to exhibit features similar to Levy walks, which in
turn have been shown to be a reasonable model of a common large scale search
strategy known as "Area Restricted Search".

Statistical Mechanics;Information Retrieval;Social and Information Networks;Physics and Society