Most of the results for laws of large numbers based on Banach space valued random sets assume that the sets are independent and identically distributed (IID), and compact, in which R̊adström embedding or the refined method for collection of compact and convex subsets of a Banach space plays an important role. In this paper, exchangeability among random sets as a dependency, instead of IID, is as...

We consider continuous-time consensus seeking systems whose time-dependent interactions are cut-balanced, in the following sense: if a group of agents influences the remaining ones, the former group is also influenced by the remaining ones by at least a proportional amount. Models involving symmetric interconnections and models in which a weighted average of the agent values is conserved are sp...

In this paper we give two examples of evanescent Markov chains which exhibit unusual behaviour on conditioning to survive for large times. In the first example we show that the conditioned processes converge vaguely in the discrete topology to a limit with a finite lifetime, but converge weakly in the Martin topology to a non-Markovian limit. In the second example, although the family of condit...

Stack-triangulations appear as natural objects when one wants to define some families of increasing triangulations by successive additions of faces. We investigate the asymptotic behavior of rooted stack-triangulations with 2n faces under two different distributions. We show that the uniform distribution on this set of maps converges, for a topology of local convergence, to a distribution on th...

taking into consideration the fact that convergence of the kurds and shiites on the national security and interests of the islamic republic of iran is a vital necessity, the exact knowledge of nature and category of such a coalition might assist the state security policymaking so that by a better understanding of such a strategy and by comprehension of sensitivity of this opportunity, the polic...

We study the convergence of consensus algorithms in wireless sensor networks with random topologies where the instantaneous links exist with a given probability and are allowed to be spatially correlated. Aiming at minimizing the convergence time of the algorithm, we adopt an optimization criterion based on the spectral radius of a positive semidefinite matrix for which we derive closed-form ex...

We analyze an entry game with multiple periods, in each period of which privately informed agents who have not joined yet decide whether to subscribe to a network, and subscribers derive benefits in future periods depending on the network size. We study the case that the agents are sufficiently patient and show that there exists a unique symmetric equilibrium if the number of existing subscribe...