Related papers: Mean Field Approximation to a Spatial Host-Pathoge…
Recent works have shown that the contact process running on the top of highly heterogeneous random networks is described by the heterogeneous mean-field theory. However, some important aspects as the transition point and strong corrections…
We use the annealed formulation of complex networks to study the dynamical behavior of disease spreading on both static and adaptive networked systems. This unifying approach relies on the annealed adjacency matrix, representing one network…
The stacked contact process is a three-state spin system that describes the co-evolution of a population of hosts together with their symbionts. In a nutshell, the hosts evolve according to a contact process while the symbionts evolve…
This work introduces a new general approach for the numerical analysis of stable equilibria to second order mean field games systems in cases where the uniqueness of solutions may fail. For the sake of simplicity, we focus on a simple…
We show under general assumptions that the mean-field approximation for quan- tum many-boson systems is correct. Our contribution unifies and improves on most of the known results. The proof uses general properties of quantization in…
Recently we have extended our the "unified" model of evolutionary ecology to incorporate the {\it spatial inhomogeneities} of the eco-system and the {\it migration} of individual organisms from one patch to another within the same…
We derive an approximate formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape inside an elongated domain of a slowly varying axisymmetric profile. For this purpose, the original Poisson equation in…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
We consider the evolution of N bosons, where N is large, with two-body interactions of the form $N^{3\beta}v(N^\beta \cdot)$, $0\leq\beta\leq 1$. The parameter $\beta$ measures the strength of interactions. We compare the exact evolution…
Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This…
In this work, we formulate an abstract framework to study mean-field systems. In contrast to most approaches in the available literature which primarily rely on the analysis of SDEs, ours is based on optimal transport and semigroup theory.…
The mean-field approximations of many-boson dynamics are known to be effective in many physical relevant situations. The mathematical justifications of such approximations rely generally on specific considerations which depend too much on…
The phase behavior of the primitive model of electrolytes is studied in the framework of various mean field approximations obtained recently by means of methods pertaining to statistical field theory (CAILLOL, J.-M., 2004, \textit{J. Stat.…
We present an exact field theoretical representation of the statistical mechanics of simple classical liquids with short-ranged pairwise additive interactions. The action of the field theory is obtained by performing a Hubbard-Stratonovich…
Since the development of generalized gradient approximations in the 1990s, approximations based on density functional theory have dominated electronic structure theory calculations. Modern approximations can yield energy differences that…
We develop a modular mean field theory for a minimalistic model of the idiotypic network. The model comprises the random influx of new idiotypes and a deterministic selection. It describes the evolution of the idiotypic network towards…
The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…
The mean-field reaction-diffusion equations of the diffusive pair-annihilation and triplett-annihilation processes are considered. A direct lower bound on the time-dependent mean particle-density is derived. The results are applied to the…
Despite being similar in structure, functioning, and size viral pathogens enjoy very different mostly well-defined ways of life. They occupy their hosts for a few days (influenza), for a few weeks (measles), or even lifelong (HCV), which…
A mean field argument is used to derive a master equation for systems simultaneously interacting with external fields and coupled environmental degrees of freedom. We prove that this master equation preserves positivity of the reduced…