Related papers: Large population limits of Markov processes on ran…
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 on the introduction of an annealed approximation for…
This paper deals with the derivation of the mean-field limit for multi-agent systems on a large class of sparse graphs. More specifically, the case of non-exchangeable multi-agent systems consisting of non-identical agents is addressed. The…
Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with multiple invariant measures}. We consider both the case in…
We establish new conditions for obtaining uniform bounds on the moments of discrete-time stochastic processes. Our results require a weak negative drift criterion along with a state-dependent restriction on the sizes of the one-step jumps…
The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…
We study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic…
We study the statistical properties of population dynamics evolving in a realistic two-dimensional compressible turbulent velocity field. We show that the interplay between turbulent dynamics and population growth and saturation leads to…
We consider a general class of Markovian models describing the growth in a randomly fluctuating environment of a clonal biological population having several phenotypes related by stochastic switching. Phenotypes differ e.g. by the level of…
Population dynamics provides a numerical tool allowing for the study of rare events by means of simulating a large number of copies of the system, supplemented with a selection rule that favours the rare trajectories of interest. The…
A broad range of dynamical systems involve multi-body interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, the Majority Rule,…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
The theory of Balanced Neural Networks is a very popular explanation for the high degree of variability and stochasticity in the brain's activity. Roughly speaking, it entails that typical neurons receive many excitatory and inhibitory…
In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…
Temporal social networks of human interactions are preponderant in understanding the fundamental patterns of human behavior. In these networks, interactions occur locally between individuals (i.e., nodes) who connect with each other at…
The dynamics of well-mixed biological populations is usually studied by mean-field methods and weak-noise expansions. Similar methods have been applied also in spatially extended problems, relying on the fact that these populations are…
In this work, it is pointed out that in the mean-field version of majority-rule opinion dynamics, the dependence of the consensus time on the population size exhibits two regimes. This is determined by the size distribution of the groups…
We present a stochastic model of population dynamics exploiting cross-sectional data in trend analysis and forecasts for groups and cohorts of a population. While sharing the convenient features of classic Markov models, it alleviates the…
We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To…
We review the statistical mechanics approach to the study of the emerging collective behavior of systems of heterogeneous interacting agents. The general framework is presented through examples is such contexts as ecosystem dynamics and…
There exists a wide variety of works on the dynamics of large populations ranging from simple heuristic modeling to those based on advanced computer supported methods. Their interconnections, however, remain mostly vague, which…