Related papers: The mean-field Zero-Range process with unbounded m…
This paper is concerned with the convergence rates of subsonic flows for airfoil problem and infinite long largely-open nozzle problem, which is an improvement of [7,11,15,20]. The maximum principle is applied to estimate the potential…
We consider the dynamics of the disordered, one-dimensional, symmetric zero range process in which a particle from an occupied site $k$ hops to its nearest neighbour with a quenched rate $w(k)$. These rates are chosen randomly from the…
Zero-range effective interactions are commonly used in nuclear physics and in other domains to describe many-body systems within the mean-field model. If they are used within a beyond-mean-field framework, contributions to the total energy…
We show how the central equality of scattering theory, the definition of the $\mathbb{T}$ operator, can be used to generate hierarchies of mean-field constraints that act as natural complements to the standard electromagnetic design problem…
We investigate a zero-range process where the underlying one-particle stationary distribution has multifractality. The multiparticle stationary probability measure can be written in a factorized form. If the number of the particles is…
We consider a generalized one-dimensional chain in a periodic potential (the Frenkel-Kontorova model), with dissipative, pulsating (or ratchet) dynamics as a model of transport when the average force on the system is zero. We find lower…
We provide an extension of the method of asymptotic decompositions of vector fields with finite-time singularities by applying the central extension technique of Poincar\'e to the dominant part of the vector field on approach to the…
We study the mean-field theory, and the properties of fluctuations, in an out of equilibrium Bose-Fermi system, across the transition to a quantum condensed phase. The system is driven out of equilibrium by coupling to multiple baths, which…
We investigate the mixing properties of a finite Markov chain in random environment defined as a mixture of a deterministic chain and a chain whose state space has been permuted uniformly at random. This work is the counterpart of a…
The method of zero-range potentials is generalized to account for the molecular electron excitation process. It is made by a matrix formulation in which a state vector components are associated with a scattering channel. The multi-center…
We estimate the distance in total variation between the law of a finite state Markov process at time t, starting from a given initial measure, and its unique invariant measure. We derive upper bounds for the time to reach the equilibrium.…
A collection of rigorous results for a class of mean-field monomer-dimer models is presented. It includes a Gaussian representation for the partition function that is shown to considerably simplify the proofs. The solutions of the quenched…
Monte Carlo simulations of finite density systems are often plagued by the complex action problem. We point out that there exists certain non-commutativity in the zero chemical potential limit and the thermodynamic limit when one tries to…
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal…
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal…
Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. This paper considers the long-standing debate over finite mixture and infinite mixtures and brings the two modelling…
Zero-range effective interactions are commonly used in nuclear physics to describe a many-body system in the mean-field framework. If they are employed in beyond- mean-field models, an artificial ultraviolet divergence is generated by the…
The theory of boundary regularity for $p$-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality, $1<p<\infty$. The barrier classification of regular…
We prove the chain rule in the more general framework of the Wiener-Poisson space, allowing us to obtain the so-called Nourdin-Peccati bound. From this bound we obtain a second-order Poincare-type inequality that is useful in terms of…
We study the mean-field dynamics of a system of $N$ interacting bosons starting from an initially condensated state. For a broad class of mean-field Hamiltonians, including models with arbitrary bounded interactions and models with…