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Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as $n$ interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or…
The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time…
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…
A principled method to obtain approximate solutions of general constrained integer optimization problems is introduced. The approach is based on the calculation of a mean field probability distribution for the decision variables which is…
We review some possible improvements of mean field theory for application to nuclear binding systematics. Up to now, microscopic theory has been less successful than models starting from the liquid drop in describing accurately the global…
We develop a mean-field description including spatial structure for a simplified version of the three-state active matter model studied by Venzel et al. (Phys. Rev. E 110, 014109 (2024)). The resulting triangular lattice of coupled…
We present a study of a phase-separation process induced by the presence of spatially-correlated multiplicative noise. We develop a mean-field approach suitable for conserved-order-parameter systems and use it to obtain the phase diagram of…
Mean Field inference is central to statistical physics. It has attracted much interest in the Computer Vision community to efficiently solve problems expressible in terms of large Conditional Random Fields. However, since it models the…
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…
Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a…
A general self-consistency approach allows a thorough treatment of the corrections to the mean-field approximation (MFA). The natural extension of standard MFA with the help of a cumulant expansion leads to a new point of view on the…
A quantum field theoretic formulation of the dynamics of the Contact Process on a regular graph of degree z is introduced. A perturbative calculation in powers of 1/z of the effective potential for the density of particles phi(t) and an…
Mean field approximation is a powerful technique which has been used in many settings to study large-scale stochastic systems. In the case of two-timescale systems, the approximation is obtained by a combination of scaling arguments and the…
Mean field theory models of percolation on networks provide analytic estimates of network robustness under node or edge removal. We introduce a new mean field theory model based on generating functions that includes information about the…
Mean-field theory is an approximation replacing an extended system by a few variables. For depinning of elastic manifolds, these are the position of its center of mass $u$, and the statistics of the forces $F(u)$. There are two proposals to…
This paper studies the rate of convergence of a family of continuous-time Markov chains (CTMC) to a mean-field model. When the mean-field model is a finite-dimensional dynamical system with a unique equilibrium point, an analysis based on…
We introduce a mean-field and perturbative approach, based on clusters, to describe the ground state of fermionic strongly-correlated systems. In cluster mean-field, the ground state wavefunction is written as a simple tensor product over…
A general self-consistency approach allows a thorough treatment of the corrections to the standard mean-field approximation (MFA). The natural extension of standard MFA with the help of a cumulant expansion leads to a new point of view on…
{Full three dimensional static and dynamic mean field calculations using collocation basis splines with a Skyrme type Hamiltonian are described. This program is developed to address the difficult theoretical challenges offered by exotic…
A novel, exact, theoretical method for the study of the excited states of a system is presented. It is demonstrated how to transform the excited state problem of one Hamiltonian into the ground state problem of an auxiliary one. From this,…