Related papers: Mean Field Approximation to a Spatial Host-Pathoge…
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…
In this paper, we consider the Hamiltonian evolution of N weakly interacting Bosons. Assuming triple collisions, its mean field approximation is given by a quintic Hartree equation. We construct a second order correction to the mean field…
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…
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…
We are interested in the invasion phase for stochastic processes with interactions when a single mutant with positive fitness arrives in a resident population at equilibrium. By a now classic approach, the first stage of the invasion is…
We consider the spherical model on a spider-web graph. This graph is effectively infinite-dimensional, similar to the Bethe lattice, but has loops. We show that these lead to non-trivial corrections to the simple mean-field behavior. We…
This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…
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…
Here, we consider one-dimensional forward-forward mean-field games (MFGs) with congestion, which were introduced to approximate stationary MFGs. We use methods from the theory of conservation laws to examine the qualitative properties of…
We investigate the influence of the adjustment procedure and the set of measured observables on the properties and predictive power of relativistic self-consistent mean-field models for the nuclear ground state. These studies are performed…
The spread of infectious disease and the evolution of antigenically distinct strains are often modeled separately, despite strong feedbacks mediated by host immune memory and heterogeneous contacts. To tackle this challenging problem, we…
Invasive pine trees pose a threat to biodiversity in a variety of Southern Hemisphere countries, but understanding of the dynamics of invasions and the factors that retard or accelerate spread is limited. Here, we consider the past models…
The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Some examples are…
Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…
The now classical replicator equation describes a wide variety of biological phenomena, including those in theoretical genetics, evolutionary game theory, or in the theories of the origin of life. Among other questions, the permanence of…
Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An…
We introduce a generalized version of the frog model to describe the invasion of a parasite population in a spatially structured immobile host population with host immunity on the integer line. Parasites move according to simple symmetric…
This paper is concerned with developing mean-field game models for the evolution of epidemics. Specifically, an agent's decision -- to be socially active in the midst of an epidemic -- is modeled as a mean-field game with health-related…
This paper proves the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full rigorous derivation (with quantitative estimates) of the…
We study the competition between random multiplicative growth and redistribution/migration in the mean-field limit, when the number of sites is very large but finite. We find that for static random growth rates, migration should be strong…