Related papers: On Approximations and Ergodicity Classes in Random…
We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…
The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route…
The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…
Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…
This article studies the convergence properties of trans-dimensional MCMC algorithms when the total number of models is finite. It is shown that, for reversible and some non-reversible trans-dimensional Markov chains, under mild conditions,…
Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In this paper we study an ergodic model for random population…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
We show that there are two classes of finite size effects for dynamic models taking place on a scale-free topology. Some models in finite networks show a behavior that depends only on the system size N. Others present an additional distinct…
We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical…
Randomized load balancing networks arise in a variety of applications, and allow for efficient sharing of resources, while being relatively easy to implement. We consider a network of parallel queues in which incoming jobs with independent…
We obtain a perfect sampling characterization of weak ergodicity for backward products of finite stochastic matrices, and equivalently, simultaneous tail triviality of the corresponding nonhomogeneous Markov chains. Applying these ideas to…
We study some percolation problems on the complete graph over $\mathbf N$. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
In this paper, we give quantitative bounds on the $f$-total variation distance from convergence of an Harris recurrent Markov chain on an arbitrary under drift and minorisation conditions implying ergodicity at a sub-geometric rate. These…
Generating long-term trajectories of dissipative chaotic systems autoregressively is a highly challenging task. The inherent positive Lyapunov exponents amplify prediction errors over time. Many chaotic systems possess a crucial property -…
The paper provides a systematic characterization of quantum ergodic and mixing channels in finite dimensions and a discussion of their structural properties. In particular, we discuss ergodicity in the general case where the fixed point of…
We study ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching. The first set of results concerns the ergodic properties of the properly scaled joint Markov process with a parameter that…
The use of higher-order stochastic processes such as nonlinear Markov chains or vertex-reinforced random walks is significantly growing in recent years as they are much better at modeling high dimensional data and nonlinear dynamics in…
We introduce a probabilistic framework that represents stylized banking networks with the aim of predicting the size of contagion events. Most previous work on random financial networks assumes independent connections between banks, whereas…
Deterministic dynamical systems such as the baker maps are useful to shed light on some of the conditions verified by deterministic models in non-equilibrium statistical physics. We investigate a 2D dynamical system, enjoying a weak form of…