Related papers: Recent Applications of Dynamical Mean-Field Method…
Despite the diversity of materials designated as active matter, virtually all active systems undergo a form of dynamic arrest when crowding and activity compete, reminiscent of the dynamic arrest observed in colloidal and molecular fluids…
We study the off equilibrium dynamics of a mean field disordered systems which can be interpreted both as a long range interaction spin glass and as a particle in a random potential. The statics of this problem is well known and exhibits a…
Finite lattice models are a prototype for strongly correlated quantum systems and capture essential properties of condensed matter systems. With the dramatic progress in ultracold atoms in optical lattices, finite fermionic Hubbard systems…
The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…
We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description…
The glass transition, extensively studied in dense fluids, polymers, or colloids, corresponds to a dramatic evolution of equilibrium transport coefficients upon a modest change of control parameter, like temperature or pressure. A similar…
We introduce and study a nonlinear discrete dynamical system describing the evolution of a resource distribution among interacting agents. The model generalizes several classical mean-field and opinion-dynamics frameworks and is defined on…
Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex systems. As their behavior is not tractable for large networks, many mean-field methods have been proposed for their analysis, each based on unique…
We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical…
Dynamics is central to living systems. In the last two decades, experiments have revealed that the dynamics in diverse biological systems - from intracellular cytoplasm to cellular and organismal aggregates - are remarkably similar to that…
Systems of interacting objects often evolve under the influence of field effects that govern their dynamics, yet previous works have abstracted away from such effects, and assume that systems evolve in a vacuum. In this work, we focus on…
Motivated by the climate crisis that is currently ravaging the planet, we propose and analyze a novel framework for the evolution of anthropogenic climate impact in which the evolution of human environmental behavior and environmental…
Dynamical Mean-Field Theory (DMFT) has established itself as a reliable and well-controlled approximation to study correlation effects in bulk solids and also two-dimensional systems. In combination with standard density-functional theory…
In this report, I will review some of the most used models in theoretical ecology along with appealing reformulations and recent results in terms of diversity, stability, and functioning of large well-mixed ecological communities.
Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this…
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…
Despite the knowledge that social, economical, and ecological networks are often of a small-world nature with inter-nodal distance growing even slower than logarithmically with system size, we often assume theoretical systems to be outside…
We present a unified field-theoretic framework for the dynamics of activity and connectivity in interacting neuronal systems. Building upon previous works, where a field approach to activity--connectivity dynamics, formation of collective…
Many active matter systems, especially on the microscopic scale, are well approximated as overdamped, meaning that any inertial momentum is immediately dissipated by the environment. On the other hand, especially for macroscopic active…
Mean field approximation is a popular method to study the behaviour of stochastic models composed of a large number of interacting objects. When the objects are asynchronous, the mean field approximation of a population model can be…