One-dimensional harmonic lattice caricature of hydrodynamics: Second approximation

The long-time behavior of an infinite chain of coupled harmonic oscillators is studied. In addition to a limiting hydrodynamic (Euler-type) equation, the next approximation is investigated. The corresponding equation is derived.     

Stationary solutions of the bogoliubov hierarchy equations in classical statistical mechanics. 2

In the preceding paper under the same title we have formulated a theorem which describes the set of states (i.e., probability measures on phase space of an infinite system of particles inR ^v) corresponding to stationary solutions of the BBGKY hierarchy. We have proved the following statement: ifG is a Gibbs measure (Gibbs random point field) corresponding to a stationary solution of the BBGKY hierarchy, then its generating function satisfies a differential equation which is conjugated to the BBGKY hierarchy. The present paper deals with the investigation of the conjugated equation for the generating function in particular cases.     

Entropy and Random Vectors

Barron⁽¹⁾ produced a proof of the Central Limit Theorem for real-valued IID random variables, in the sense of convergence in relative entropy. Here, we establish a similar result for independent real-valued random vectors, not necessarily identically distributed. The main developments required are a generalisation of De Bruijn's identity, and various inequalities proposed in ref. 2.     

Stationary solutions of the Bogoliubov hierarchy equations in classical statistical mechanics. 4

This is the forth and final paper of a series in which we investigate the stationary solutions of the BBGKY equations. Herein we prove a lemma which forms the basic step in the proof of our Main Theorem characterizing the stationary solutions of these equations which was stated in the first of this series.     

Random point processes and DLR equations

We prove the uniqueness of a solution of the Dobrushin-Lanford-Ruelle equation for random point processes when the generating function (interaction potential) has no hard cores, is non-negative and rapidely decreasing.     

Eigenfunctions in a Two-Particle Anderson Tight Binding Model

We establish the phenomenon of Anderson localisation for a quantum two-particle system on a lattice with short-range interaction and in presence of an IID external potential with sufficiently regular marginal distribution.     

A mean-field limit for a class of queueing networks

A model of centralized symmetric message-switched networks is considered, where the messages having a common address must be served in the central node in the order which corresponds to their epochs of arrival to the network. The limitN is discussed, whereN is the branching number of the network graph. This procedure is inspired by an analogy with statistical mechanics (the mean-field approximation). The corresponding limit theorems are established and the limiting probability distribution for the network response time is obtained. Properties of this distribution are discussed in terms of an associated boundary problem.     

Weighted Gaussian entropy and determinant inequalities

Aequationes mathematicae - We produce a series of results extending information-theoretical inequalities (discussed by Dembo–Cover–Thomas in 1988–1991) to a weighted version of...