Related papers: Quantitative convergence in relative entropy for a…
We show that the Kac particle system converges, as the number of particles tends to infinity, to the solution of the homogeneous Boltzmann equation, in the regime of moderately soft potentials, $\gamma \in (-2,0)$ with the common notation.…
The aim is to assess the combined effect of diffusion and dispersion on shocks in the moderate dispersion regime. For a diffusive dispersive approximation of the equations of one-dimensional elasticity (or p-system), we study convergence of…
We give a new proof of the large deviation principle from the hydrodynamic limit for the Ginzberg-Landau model studied in Donsker and Varadhan (1989) using techniques from the theory of stochastic control and weak convergence methods. The…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
In this paper, we analyse the rate of convergence of a system of $N$ interacting particles with mean-field rank based interaction in the drift coefficient and constant diffusion coefficient. We first adapt arguments by Kolli and Shkolnikhov…
We show how to obtain general nonlinear aggregation-diffusion models, including Keller-Segel type models with nonlinear diffusions, as relaxations from nonlocal compressible Euler-type hydrodynamic systems via the relative entropy method.…
The Random Batch Method proposed in our previous work [Jin et al., J. Comput. Phys., 400(1), 2020] is not only a numerical method for interacting particle systems and its mean-field limit, but also can be viewed as a model of particle…
The couplings by change of measure are applied to establish log-Harnack inequality(equivalently the entropy-cost estimate) for conditional McKean-Vlasov SDEs and derive the quantitative conditional propagation of chaos in relative entropy…
We consider interacting particle systems with unbounded interaction range on general countably infinite graphs $S$ and prove explicit non-asymptotic error bounds for approximations of the infinite-volume dynamics by systems of finitely many…
We study fluid structure and water-like anomalies of a system constituted by dimeric particles interacting via a purely repulsive core-softened potential by means of integral equation theories. In our model, dimers interact through a…
Coherent propagation of two interacting particles in $1d$ weak random potential is considered. An accurate estimate of the matrix element of interaction in the basis of localized states leads to mapping onto the relevant matrix model. This…
The aim of the paper is to establish a large deviation principle (LDP) for the empirical measure of mean-field interacting diffusions in a random environment. The point is to derive such a result once the environment has been frozen…
There is a vast body of recent literature on the reliability of communication through noisy channels, the recovery of community structures in the stochastic block model, the limiting behavior of the free entropy in spin glasses and the…
Relative entropy serves as a cornerstone concept in quantum information theory. In this work, we study relative entropy of random states from major generic state models of Hilbert-Schmidt and Bures-Hall ensembles. In particular, we derive…
We study the capacity of entanglement in certain integrable scale-invariant theories which exhibit Lifshitz scaling symmetry with a generic dynamical exponent z at the critical point. This measure characterizes the width of the eigenvalue…
We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…
Although most studies of strongly correlated systems away from equilibrium have focused on clean systems, it is well known that disorder may significantly modify observed properties in various nontrivial ways. The nonequilibrium interplay…
The quantum relative entropy is a fundamental quantity in quantum information science, characterizing the distinguishability between two quantum states. However, this quantity is not additive in general for correlated quantum states,…
For any weakly interacting particle system with bounded kernel, we give uniform-in-time estimates of the $L^2$ norm of correlation functions, provided that the diffusion coefficient is large enough. When the condition on the kernels is more…
A new closure of the BBGKY hierarchy is developed, which results in a convergent kinetic equation that provides a rigorous extension of plasma kinetic theory into the regime of strong Coulomb coupling. The approach is based on a single…