Chapter: First-Passage Phenomena on Finite Inhomogeneous Networks
A sequence of strongly inhomogeneous networks, with increasing sizes, can lead to very different thermodynamic limits, depending on the site chosen as the origin. This singular behavior reflects in remarkable phenomena even at finite sizes. Indeed, the finite networks belonging to such sequences, even with a small number of sites, presents significant inhomogeneities in first-passage related quantities, depending on the starting site of the random walker. This kind of behavior is of primary importance for the understanding of diffusion phenomena on real inhomogeneous systems, which are finite and cannot be univocally described by an infinite structure in the thermodynamic limit. Here, we explore the properties of the above mentioned quantities on a collection of the most typical and known inhomogeneous finite networks, both analytically and numerically, evidencing their unique features.