Related papers: Replica-Mean-Field Limits of Fragmentation-Interac…
Many phenomena can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this difficulty, the Poisson Hypothesis regime replaces interaction…
Neural computations arising from myriads of interactions between spiking neurons can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this…
Neural computations emerge from myriads of neuronal interactions occurring in intricate spiking networks. Due to the inherent complexity of neural models, relating the spiking activity of a network to its structure requires simplifying…
Replica-mean-field models have been proposed to decipher the activity of neural networks via a multiply-and-conquer approach. In this approach, one considers limit networks made of infinitely many replicas with the same basic neural…
We study mean-field descriptions for spatially-extended networks of linear (leaky) and quadratic integrate-and-fire neurons with stochastic spiking times. We consider large-population limits of continuous-time Galves-L\"ocherbach (GL)…
Interacting particle systems can often be constructed from a graphical representation, by applying local maps at the times of associated Poisson processes. This leads to a natural coupling of systems started in different initial states. We…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
In this paper we prove the Poisson Hypothesis for the limiting behavior of the large queueing systems in some simple ("mean-field") cases. We show in particular that the corresponding dynamical systems, defined by the non-linear Markov…
We study the mean-field limit of a generic class of dynamic co-evolving latent space networks motivated by the social and opinion dynamics literature. Such models include $n$ agents, whose opinions are given by latent stochastic processes,…
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…
Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or…
We study Replica Mean Field limits for a neural system of infinitely many neurons with both inhibitory and excitatory interactions. As a result we obtain an analytical characterisation of the invariant state. In particular we focus on the…
In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form a Poisson clustered…
We investigate a spatial random graph model whose vertices are given as a marked Poisson process on $\mathbb{R}^d$. Edges are inserted between any pair of points independently with probability depending on the spatial displacement of the…
We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…
We prove that the general mean-field type networks at low load behave in accordance with the Poisson Hypothesis. That means that the network equilibrates in time independent of its size. This is a "high-temperature" counterpart of our…
We study the random connection model driven by a stationary Poisson process. In the first part of the paper, we derive a lace expansion with remainder term in the continuum and bound the coefficients using a new version of the BK…
We study the mean-field limit of a model of biological neuron networks based on the so-called stochastic integrate-and-fire (IF) dynamics. Our approach allows to derive a continuous limit for the macroscopic behavior of the system, the…
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…
Many real-world phenomena can be modelled as dynamical processes on networks, a prominent example being the spread of infectious diseases such as COVID-19. Mean-field approximations are a widely used tool to analyse such dynamical processes…