Multicanonical MCMC (Multicanonical Markov Chain Monte Carlo; Multicanonical Monte Carlo) is discussed as a method of rare event sampling. Starting from a review of the generic framework of importance sampling, multicanonical MCMC is introduced, followed by applications in random matrices,...

Motivated by the desire to model internet traffic we consider random walks that start and are absorbed on the leaves of random networks and study the length of such walks. We present and test two techniques to analyse these walks. On Erdős–Rényi random graphs where the probability of a walk...

What triggers the information exchange among the regional offices in Brussels? To answer this question, we develop a framework based on network theory and present the first large-N quantitative study on European Union-level inter-regional networks. Our results show that information exchanges...

We consider a long-range percolation on a vertex set of a two-dimensional square lattice, where the probabilities that horizontally long bonds exist may be different from the probabilities that vertically long bonds exist. We give some estimates on the effective resistance in such a model. The...