Target decay on irregular networks

Abstract

We investigate the survival probability of immobile targets, which get annihilated by randomwalkers (RWs) at first encounter. We focus on scale-free networks (SFNs) and on smallworld networks (SWNs) as examples of irregular lattices. On SFNs we consider degreedistributions (DDs) with long time tails. Interestingly, it turns out that the survival probabilityand the quality of its description through the average number of distinct sites visited,Sn, depend on the details of the DD: SFNs which are more ramified have survivalprobabilities which are more regular, whereas SFNs with long chain-like segmentsdisplay decay laws similar to those of SWNs, where a description only in terms ofSn is rather poor.