Related papers: Correlation estimates for Brownian particles with …
We survey the current status of universality limits for $m$-point correlation functions in the bulk and at the edge for unitary ensembles, primarily when the limiting kernels are Airy, Bessel, or Sine kernels. In particular, we consider…
The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two…
We study the existence and the exponential ergodicity of a general interacting particle system, whose components are driven by independent diffusion processes with values in an open subset of $\mathds{R}^d$, $d\geq 1$. The interaction…
Quantum many-body systems realise many different phases of matter characterised by their exotic emergent phenomena. While some simple versions of these properties can occur in systems of free fermions, their occurrence generally implies…
We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…
We prove a rigorous lower bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of singular interactions, including the Coulomb potential. Combined with the upper bound obtained in…
We study the mean-field limit of a model of biological neuron networks based on the so-called stochastic integrate-and-fire (IF) dynamics. Our approach allows to derive a continuous limit for the macroscopic behavior of the system, the…
Applying a variational multiparticle-multihole configuration mixing method whose purpose is to include correlations beyond the mean field in a unified way without particle number and Pauli principle violations, we investigate pairing-like…
Following the paradigm of Boltzmann-BBGKY we propose a correlation entropy (of the nth order) for an interacting quantum field, obtained by `slaving' (truncation with causal factorization) of the higher (n+1 th) order correlation functions…
We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…
We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…
In this first in a series of articles, we apply effective interactions derived by the Unitary Correlation Operator Method (UCOM) to the description of open-shell nuclei, using a self-consistent Hartree-Fock-Bogoliubov framework to account…
In this article, we study the parameter estimation of interacting particle systems subject to the Newtonian aggregation and Brownian diffusion. Specifically, we construct an estimator $\widehat{\nu}$ with partial observed data to…
In the past decade, natural orbital functional (NOF) approximations have emerged as prominent tools for characterizing electron correlation. Despite their effectiveness, these approaches, which rely on natural orbitals and their associated…
We discuss the pairing gap, a measure for nuclear pairing correlations, in chains of spherical, semi-magic nuclei in the framework of self-consistent nuclear mean-field models. The equations for the conventional BCS model and the…
Quantifying correlation and complexity in quantum many-body states is central to advancing theoretical and computational chemistry, physics, and quantum information science. This work introduces a novel framework, mutual correlation, based…
We discuss the treatment, in an effective field theory, of multi-particle correlations within a "large" system. We show that the act of coarse-graining necessarily introduces violations of unitarity in the evolution of states where the…
Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…
In a weakly correlated inhomogeneous plasma an equation of pair correlation function is obtained utilizing the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations. In this article the pair correlation function has been…
We present a diagrammatic formulation of a theory for the time dependence of density fluctuations in equilibrium systems of interacting Brownian particles. To facilitate derivation of the diagrammatic expansion we introduce a basis that…