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Understanding information exchange and aggregation on networks is a central problem in theoretical economics, probability and statistics. We study a standard model of economic agents on the nodes of a social network graph who learn a binary…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
We consider the Ising model for two interacting groups of spins embedded in an Erd\"{o}s-R\'{e}nyi random graph. The critical properties of the system are investigated by means of extensive Monte Carlo simulations. Our results evidence the…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
We study a discrete-time consensus model in which agents iteratively update their states through interactions on a dynamic social network. At each step, a single agent is selected asynchronously and averages the values of its current…
We study the properties of a subclass of stochastic processes called discrete time nonlinear Markov chains with an aggregator, which naturally appear in various topics such as strategic queueing systems, inventory dynamics, opinion…
In this paper, we study the global dynamics of epidemic network models with standard incidence or mass-action transmission mechanism, when the dispersal of either the susceptible or the infected people is controlled. The connectivity matrix…
Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the…
Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological,…
In previous work, we developed the scaled SIS process, which models the dynamics of SIS epidemics over networks. With the scaled SIS process, we can consider networks that are finite-sized and of arbitrary topology (i.e., we are not…
With the premise that social interactions are described by power-law distributions, we study a SIR stochastic dynamic on a static scale-free random network generated via configuration model. We verify our model with respect to deterministic…
We consider a class of particle systems described by differential equations (both stochastic and deterministic), in which the interaction network is determined by the realization of an Erd\H{o}s-R\'enyi graph with parameter $p_n\in (0, 1]$,…
We demonstrate a vast expansion of the theory of evolutionary stability to finite populations with mutation, connecting the theory of the stationary distribution of the Moran process with the Lyapunov theory of evolutionary stability. We…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
We study the dynamics of the Stochastic Sandpile Model on finite graphs, with two main results. First, we describe a procedure to exactly sample from the stationary distribution of the model in all connected finite graphs, extending a…
Stochastic large scale interacting systems can be studied via the observables, i.e. functions on the underlying configuration space. In our previous article, we introduced the concept of uniform functions, which are suitable class of…
Nonlinear Markov chains with finite state space have been introduced in Kolokoltsov (2010). The characteristic property of these processes is that the transition probabilities do not only depend on the state, but also on the distribution of…
The statistical properties of pairwise majority voting over S alternatives is analyzed in an infinite random population. We first compute the probability that the majority is transitive (i.e. that if it prefers A to B to C, then it prefers…
In some systems, the behavior of the constituent units can create a `context' that modifies the direct interactions among them. This mechanism of indirect modification inspired us to develop a minimal model of context-dependent spreading.…
This paper investigates multi-agent frequencybased patrolling of intersecting, circle graphs under conditions where graph nodes have non-uniform visitation requirements and agents have limited ability to communicate. The task is modeled as…