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

Many science phenomena are described as interacting particle systems (IPS). The mean
field limit (MFL) of large all-to-all coupled deterministic IPS is given by the solution of a PDE …

In this paper we propose a framework to investigate the mean field limit (MFL) of interacting
particle systems on directed hypergraphs. We provide a non-trivial measure-theoretic …

In this article we report on a novel way to incorporate complex network structure into the
analysis of interacting particle systems. More precisely, it is well-known that in well …

Many science phenomena are modelled as interacting particle systems (IPS) coupled on
static networks. In reality, network connections are far more dynamic. Connections among …

We investigate the mean-field dynamics of stochastic McKean differential equations with
heterogeneous particle interactions described by large network structures. To express a …

We consider a class of weakly interacting particle systems of mean-field type. The
interactions between the particles are encoded in a graph sequence, ie two particles are …

We consider a system of $ N $ particles whose interactions are characterized by a
(weighted) graph $ G^ N $. Each particle is a node of the graph with an internal state. The …

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 …

Originally arising in the context of interacting particle systems in statistical physics,
dynamical systems and differential equations on networks/graphs have permeated into a …