相关论文: Mean-field limits in interacting particle systems …

Exchange-driven growth (EDG) is a process in which pairs of clusters interact by exchanging single unit with a rate given by a kernel $K(j,k)$. Despite EDG model's common use in the applied sciences, its rigorous mathematical treatment is…

The exchange-driven growth (EDG) model describes the evolution of clusters through the exchange of single monomers between pairs of interacting clusters. The dynamics of this process are primarily influenced by the interaction kernel…

The continuous generalized exchange-driven growth model (CGEDG) is a system of integro-differential equations describing the evolution of cluster mass under mass exchange. The rate of exchange depends on the masses of the clusters involved…

Exchange-driven growth is a process in which pairs of clusters interact and exchange a single unit of mass. The rate of exchange is given by an interaction kernel $K(j,k)$ which depends on the masses of the two interacting clusters. In this…

Many natural phenomena are effectively described by interacting particle systems, which can be modeled using either deterministic or stochastic differential equations (SDEs). In this study, we specifically investigate particle systems…

Interacting particle systems are in frequent use to model collective behaviour in various situations and applications. For many systems, the interaction between the agents is restricted to an underlying network structure and often, the…

We establish a connection between tagged particles and size-biased empirical processes in interacting particle systems, in analogy to classical results on the propagation of chaos. In a mean-field scaling limit, the evolution of the…

The mean-field limit of interacting diffusions without exchangeability, caused by weighted interactions and non-i.i.d. initial values, are investigated. The weights could be signed and unbounded. The result applies to a large class of…

Interacting particle systems are known for their ability to generate large-scale self-organized structures from simple local interaction rules between each agent and its neighbors. In addition to studying their emergent behavior, a main…

This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that…

We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…

In this work, we consider one-dimensional particles interacting in mean-field type through a bounded kernel. In addition, when particles hit some barrier (say zero), they are removed from the system. This absorption of particles is…

The continuous generalized exchange-driven growth model (CGEDG) is a coagulation-fragmentation equation that describes the evolution of the macroscopic cluster size distribution induced by a microscopic dynamic of binary exchanges of masses…

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…

For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…

We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as…

We study a discrete model for generalized exchange-driven growth in which the particle exchanged between two clusters is not limited to be of size one. This set of models include as special cases the usual exchange-driven growth system and…

Fokker-Planck equations represent a suitable description of the finite-time behavior for a large class of particle systems as the size of the population tends to infinity. Recently, the theory of graph limits has been introduced in the…

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…

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…