Random walks are ubiquitous in the sciences, and they are interesting from both theoretical
and practical perspectives. They are one of the most fundamental types of stochastic …

We present a general theory which allows one to accurately evaluate the mean first-passage
time (FPT) for regular random walks in bounded domains, and its extensions to related first …

The availability of large data sets has allowed researchers to uncover complex properties
such as large-scale fluctuations and heterogeneities in many networks, leading to the …

We study the voter model on heterogeneous graphs. We exploit the nonconservation of the
magnetization to characterize how consensus is reached. For a network of N nodes with an …

This book discusses the study and analysis of the physical aspects of social systems and
models, inspired by the analogy with familiar models of physical systems and possible …

How long does it take a random walker to reach a given target point? This quantity, known
as a first-passage time (FPT), has led to a growing number of theoretical investigations over …

We propose a new analytical method to study stochastic, binary-state models on complex
networks. Moving beyond the usual mean-field theories, this alternative approach is based …

We present a general framework, applicable to a broad class of random walks on complex
networks, which provides a rigorous lower bound for the mean first-passage time of a …

The first passage time (FPT) for random walks is a key indicator of how fast information
diffuses in a given system. Despite the role of FPT as a fundamental feature in transport …

We consider degree-biased random walkers whose probability to move from a node to one
of its neighbors of degree k is proportional to k α, where α is a tuning parameter. We study …