Related papers: Synchronization and functional central limit theor…
We study the influence of motion on the emergence of synchronization in a metapopulation of random walkers moving on a heterogeneous network and subject to Kuramoto interactions at the network nodes. We discover a novel mechanism of…
We study general random dynamical systems of continuous maps on some compact metric space. Assuming a local contraction condition and uniqueness of the stationary measure, we establish probabilistic limit laws such as the central limit…
Real-world complex systems exhibit multiple levels of relationships. In many cases they require to be modeled as interconnected multilayer networks, characterizing interactions of several types simultaneously. It is of crucial importance in…
Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems -- yielding a Gaussian density multiplied by a highly oscillatory…
This paper addresses consensus optimization problems in a multi-agent network, where all agents collaboratively find a minimizer for the sum of their private functions. We develop a new decentralized algorithm in which each agent…
In arXiv:1609.05666v1 [math.PR] a functional limit theorem was proved. It states that symmetric processes associated with resistance metric measure spaces converge when the underlying spaces converge with respect to the…
We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…
In human crowds, interactions among individuals give rise to a variety of self-organized collective motions that help the group to effectively solve the problem of coordination. However, it is still not known exactly how humans adjust their…
Chen [Ann. Appl. Probab. {\bf 11} (2001), 1242--1262] derived exact convergence rates in a central limit theorem and a local limit theorem for a supercritical branching Wiener process.We extend Chen's results to a branching random walk…
In this article we consider transient random walks on HNN extensions of finitely generated groups. We prove that the rate of escape w.r.t. some generalised word length exists. Moreover, a central limit theorem with respect to the…
In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a…
A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This result unifies and extends previous work on repeated-interactions models, including that of the author (2010, J. London Math. Soc.…
We propose the Temporal Walk Centrality, which quantifies the importance of a node by measuring its ability to obtain and distribute information in a temporal network. In contrast to the widely-used betweenness centrality, we assume that…
Random walks in random sceneries (RWRS) are simple examples of stochastic processes in disordered media. They were introduced at the end of the 70's by Kesten-Spitzer and Borodin, motivated by the construction of new self-similar processes…
We provide complementary results for a family of models with dependence on their previous $k$-sum. Using a martingale-based approach, we establish a functional central limit theorem and analyze the limiting behavior of the center of mass.…
This work addresses synchronization in transient, non-linear stochastic dynamics corresponding to accesses performed by self-avoiding walks originating at each node of a complex network. More specifically, the synchronizability of accesses…
In this work, we establish a Trotter-Kato type theorem. More precisely, we characterize the convergence in distribution of Feller processes by examining the convergence of their generators. The main novelty lies in providing quantitative…
We construct a renewal structure for random walks on surface groups. The renewal times are defined as times when the random walks enters a particular type of a cone and never leaves it again. As a consequence, the trajectory of the random…
In this article we focus on a general model of random walk on random marked trees. We prove a recurrence criterion, analogue to the recurrence criterion proved by R. Lyons and Robin Pemantle (1992) in a slightly different model. In the…
We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models…