Related papers: Mean field limits for discrete-time dynamical syst…
We propose a cellular version of dynamical-mean field theory which gives a natural generalization of its original single-site construction and is formulated in different sets of variables. We show how non-orthogonality of the tight-binding…
We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics based on convexity of the free energy along interpolations in a…
We develop a scalable algorithm for mean field control problems with kernel interactions by combining particle system simulations with random Fourier feature approximations. The method replaces the quadratic-cost kernel evaluations by…
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been…
Multiagent reinforcement learning algorithms have not been widely adopted in large scale environments with many agents as they often scale poorly with the number of agents. Using mean field theory to aggregate agents has been proposed as a…
Large-scale systems with inherent heterogeneity often exhibit complex dynamics that are crucial for their functional properties. However, understanding how such heterogeneity shapes these dynamics remains a significant challenge,…
We derive mean-field equations for a general class of ferromagnetic spin systems with an explicit error bound in finite volumes. The proof is based on a link between the mean-field equation and the free convolution formalism of random…
A Mean-Field theory is presented and applied to a Cellular Automata model of distributed packet-switched networks. It is proved that, under a certain set of assumptions, the critical input traffic is inversely proportional to the free…
When spatial correlations are short-range, the physics of strongly correlated systems is controlled by local quantum fluctuations. In those regimes, Dynamical Mean-Field Theory can be viewed as a `compass' which provides guidance on the…
This paper studies a multi-agent system starting from a single agent dynamics which is a nonlinear affine control system. It analyze what happens when the number of agents goes to infinity using two different approaches, a granular…
We rigorously show the mean-field limit for a large class of swarming individual based models with local sharp sensitivity regions. For instance, these models include nonlocal repulsive-attractive forces locally averaged over sharp vision…
Relationships between general long-range interacting classical systems on a lattice and the corresponding mean-field models (infinitely long-range interacting models) are investigated. We study systems in arbitrary dimension d for periodic…
We study the optimal stopping problem of McKean-Vlasov diffusions when the criterion is a function of the law of the stopped process. A remarkable new feature in this setting is that the stopping time also impacts the dynamics of the…
In this paper, we derive the mean-field limit of a collective dynamics model with time-varying weights, for weight dynamics that preserve the total mass of the system as well as indistinguishability of the agents. The limit equation is a…
This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The…
Kernel mean embeddings -- integrals of a kernel with respect to a probability distribution -- are essential in Bayesian quadrature, but also widely used in other computational tools for numerical integration or for statistical inference…
The paper is concerned with the approximation of the deterministic the mean field type control system by a mean field Markov chain. It turns out that the dynamics of the distribution in the approximating system is described by a system of…
In this paper, we investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish…
This work addresses the mean-field limit of inertial particle systems with singular interactions in a perturbative regime around Gibbs equilibrium. We prove that small fluctuations around equilibrium are asymptotically governed by the…
We establish the convergence of the deep actor-critic reinforcement learning algorithm presented in [Angiuli et al., 2023a] in the setting of continuous state and action spaces with an infinite discrete-time horizon. This algorithm provides…