Related papers: Mean-field limit for collective behavior models wi…
A dynamic mean-field theory for spin ensembles (spinDMFT) at infinite temperatures on arbitrary lattices is established. The approach is introduced for an isotropic Heisenberg model with $S = \tfrac12$ and external field. For large…
Trip flow between areas is a fundamental metric for human mobility research. Given its identification with travel demand and its relevance for transportation and urban planning, many models have been developed for its estimation. These…
1. Complex systems of moving and interacting objects are ubiquitous in the natural and social sciences. Predicting their behavior often requires models that mimic these systems with sufficient accuracy, while accounting for their inherent…
Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-field theories of spin models on networks constitute a…
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…
We study an asymptotic limit of Vlasov type equation with nonlocal interaction forces where the friction terms are dominant. We provide a quantitative estimate of this large friction limit from the kinetic equation to a continuity type…
Consider a finite system of diffusing particles coupled through a reactive boundary. Each particle is reflected, but may react with the boundary according to a killing mechanism which depends on the current reactivity of the boundary and…
Repulsion between individuals within a finite radius is encountered in numerous applications, including cell exclusion, i.e. avoidance of overlapping cells, bird flocks, or microscopic pedestrian models. We define such individual based…
The well-known Cucker-Smale model is a macroscopic system reflecting flocking, i.e. the alignment of velocities in a group of autonomous agents having mutual interactions. In the present paper, we consider the mean-field limit of that…
We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighbourhood. In the first-order model the location of each…
Consider the class of Ensemble Square Root filtering algorithms for the numerical approximation of the posterior distribution of nonlinear Markovian signals partially observed with linear observations corrupted with independent measurement…
In many biological systems, motile agents exhibit random motion with short-term directional persistence, together with crowding effects arising from spatial exclusion. We formulate and study a class of lattice-based models for multiple…
We propose a large-scale scaling viewpoint for deriving mesoscopic dynamics from interacting particle systems and apply it to the Cucker--Smale flocking model. In contrast with the classical mean-field regime leading to the Vlasov-type…
Given a large ensemble of interacting particles, driven by nonlocal interactions and localized repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial differential equations known as aggregation-diffusion equations.…
Machine learning algorithms relying on deep neural networks recently allowed a great leap forward in artificial intelligence. Despite the popularity of their applications, the efficiency of these algorithms remains largely unexplained from…
We develop a new fast-diffusion approximation for the kinetics of deposition of extended objects on a linear substrate, accompanied by diffusional relaxation. This new approximation plays the role of the mean-field theory for such processes…
We address here the issue of congestion in the modeling of crowd motion, in the non-smooth framework: contacts between people are not anticipated and avoided, they actually occur, and they are explicitly taken into account in the model. We…
We introduce a Cucker-Smale-type model for flocking, where the strength of interaction between two agents depends on their relative separation (called "topological distance" in previous works), which is the number of intermediate…
This article introduces a novel approach to the mean-field limit of stochastic systems of interacting particles, leading to the first ever derivation of the mean-field limit to the Vlasov-Poisson-Fokker-Planck system for plasmas in…
We study a variant of the Cucker-Smale model where information between agents propagates with a finite speed $\mathfrak{c}>0$. This leads to a system of functional differential equations with state-dependent delay. We prove that, if…