相关论文: Generalized inequalities for the Bogoliubov-Duhame…
A new formulation of the Hamiltonian dynamics of the gravitational field interacting with(non-dissipative) thermo-elastic matter is discussed. It is based on a gauge condition which allows us to encode the six degrees of freedom of the…
We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical…
This article carries out a qualitative analysis on a system of integral equations of the Hardy--Sobolev type. Namely, results concerning Liouville type properties and the fast and slow decay rates of positive solutions for the system are…
We investigate three types of averaging principles and the normal deviation for multi-scale stochastic differential equations (in short, SDEs) with polynomial nonlinearity. More specifically, we first demonstrate the strong convergence of…
The paper contains a review of results on linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general inhomogeneous boundary conditions in Sobolev spaces. The character of the…
We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…
We introduce the concept of {\it generalized reducibility}, which provides a flexible framework for analyzing the long-time behavior of solutions to quadratic quantum Hamiltonians. As an application of this notion, for many prescribed…
We show that under a low complexity condition on the gradient of a Hamiltonian, Gibbs distributions on the Boolean hypercube are approximate mixtures of product measures whose probability vectors are critical points of an associated…
We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation…
The article builds on several recent advances in the Monge-Kantorovich theory of mass transport which have -- among other things -- led to new and quite natural proofs for a wide range of geometric inequalities such as the ones formulated…
The generalized density matrix (GDM) method is used to calculate microscopically the parameters of the collective Hamiltonian. Higher order anharmonicities are obtained consistently with the lowest order results, the mean field…
Hidden stochastic effects acting uniformly on a many-particle system can generate strong correlations and macroscopic relative fluctuations that persist at large system sizes, even when the particles themselves remain causally independent.…
We show that the Bernstein-Hoeffding method can be employed to a larger class of generalized moments. This class includes the exponential moments whose properties play a key role in the proof of a well-known inequality of Wassily Hoeffding,…
We derive an inequality relating the finite-frequency linear response and fluctuations of an observable in a physical system. The relation holds for arbitrary observables and perturbations in general Markovian dynamics, including over- and…
We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…
The paper proves generalization results for a class of stochastic learning algorithms. The method applies whenever the algorithm generates an absolutely continuous distribution relative to some a-priori measure and the Radon Nikodym…
The generalized uncertainty connection between the fluctuations of a quantum observable and its temporal derivative is derived in this study, we demonstrate that the product of an observable's uncertainties and its time derivative is…
In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…
We provide sufficient conditions for the existence of invariant probability measures for generic stochastic differential equations with finite time delay. This is achieved by means of the Krylov-Bogoliubov method. Furthermore, we focus on…
We consider Gibbs measures on the configuration space $S^{\mathbb{Z}^d}$, where mostly $d\geq 2$ and $S$ is a finite set. We start by a short review on concentration inequalities for Gibbs measures. In the Dobrushin uniqueness regime, we…