相关论文: The continuum limit of the Kuramoto model on spars…

We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…

We couple projective limits of probability measures to direct limits of their symmetry groups. We show that the direct limit group is the group of symmetries of the projective limit probability measure. If projective systems of probability…

We study the synchronisation properties of the Kuramoto model of coupled phase oscillators on a general network. Here we distinguish the ability of such a system to self-synchronise from the stability of this behaviour. While…

We investigate the mean-field dynamics of stochastic McKean differential equations with heterogeneous particle interactions described by large network structures. To express a wide range of graphs, from dense to sparse structures, we…

We rigorously derive the dense graph limit of a discrete model describing the formation of biological transportation networks. The discrete model, defined on undirected graphs with pressure-driven flows, incorporates a convex energy…

A class of evolution equations with nonlocal diffusion is considered in this work. These are integro-differential equations arising as models of propagation phenomena in continuum media with nonlocal interactions including neural tissue,…

This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…

The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…

We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent…

We present a unified framework, with quantitative estimates, for deterministic interacting particle systems whose pairwise interactions may depend on heterogeneous labels. Heterogeneity is kept at every level by adding a frozen label…

Many real-world systems of coupled agents exhibit directed interactions, meaning that the influence of an agent on another is not reciprocal. Furthermore, interactions usually do not have identical amplitude and/or sign. To describe…

This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the theory of large deviations. This is followed…

We address the issue of the proximity of interacting diffusion models on large graphs with a uniform degree property and a corresponding mean field model, i.e. a model on the complete graph with a suitably renormalized interaction…

In this paper, we study the problem of sampling from a graphical model when the model itself is changing dynamically with time. This problem derives its interest from a variety of inference, learning, and sampling settings in machine…

Large-scale networked systems typically operate under resource constraints, and it is also difficult to exactly obtain the network structure between nodes. To address these issues, this paper investigates a sparse optimal control for…

We consider the count of subgraphs with an arbitrary configuration of endpoints in the random-connection model based on a Poisson point process on ${\Bbb R}^d$. We present combinatorial expressions for the computation of the cumulants and…

We study the large-population limit of interacting particle systems evolving on adaptive dynamical networks, motivated in particular by models of opinion dynamics. In such systems, agents interact through weighted graphs whose structure…

We work out the graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function $W(x,y)$ on the unit square, with $x$ and $y$ uniform on the interval $(0,1)$.…

We introduce a framework for stochastic games on large sparse graphs, covering continuous-time and discrete-time dynamic games as well as static games. Players are indexed by the vertices of simple, locally finite graphs, allowing both…

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…