We considerN single server infinite buffer queues with service rate β. Customers arrive at rate Nα, choose L queues uniformly, and join the shortest. We study the processes t ∈ R+ 7→ R t = (R t (k))k∈N for large N , where R t (k) is the fraction of queues of length at least k at time t. Laws of large numbers (LLNs) are known, see Vvedenskaya et al. [15], Mitzenmacher [12] and Graham [5]. We con...

Architectures parall eles, Bases de donn ees, R eseaux et Syst emes distribu es Abstract Consider a polling system with K 1 queues and a single server that visits the queues in a cyclic order. The polling discipline in each queue is of general gated-type or exhaustive-type. We assume that in each queue the arrival times form a Poisson process, and that the service times, the walking times as we...

We considerN single server infinite buffer queues with service rate β. Customers arrive at rateNα, choose L queues uniformly, and join the shortest. We study the processes t ∈ R+ 7→ R t = (R t (k))k∈N for large N , where R t (k) is the fraction of queues of length at least k at time t. Laws of large numbers (LLNs) are known, see Vvedenskaya et al. [15], Mitzenmacher [12] and Graham [5]. We cons...

The idealized mode-coupling theory (MCT) is applied to colloidal systems interacting via short-range attractive interactions of Yukawa form. At low temperatures, MCT predicts a slowing down of the local dynamics and ergodicity-breaking transitions. The non-ergodicity transitions share many features with the colloidal gel transition, and are proposed to be the source of gelation in colloidal sys...

Two-dimensional (2-D) homogeneous magnetohydrodynamic (MHD) turbulence has many of the same qualitative features as three-dimensional (3-D) homogeneous MHD turbulence. These features include several ideal invariants, along with the phenomenon of broken ergodicity. Broken ergodicity appears when certain modes act like random variables with mean values that are large compared to their standard de...

The rate of quantum ergodicity is studied for three strongly chaotic (Anosov) systems. The quantal eigenfunctions on a compact Riemannian surface of genus g = 2 and of two triangular billiards on a surface of constant negative curvature are investigated. One of the triangular billiards belongs to the class of arithmetic systems. There are no peculiarities observed in the arithmetic system conce...

We introduce a generalized d-dimensional Fermi-Pasta-Ulam model in the presence of long-range interactions, and perform a first-principle study of its chaos for d=1,2,3 through large-scale numerical simulations. The nonlinear interaction is assumed to decay algebraically as d_{ij}^{-α} (α≥0), {d_{ij}} being the distances between N oscillator sites. Starting from random initial conditions we com...

The Edwards hypothesis of ergodicity of blocked configurations for gently tapped granular materials is tested for abstract models of spin systems on random graphs and spin chains with kinetic constraints. The tapping dynamics is modeled by considering two distinct mechanisms of energy injection: thermal and random tapping. We find that ergodicity depends upon the tapping procedure (i.e. the way...

In this paper, we consider time-homogeneous and asymptotically space-homogeneous Markov chains that take values on the real line and have an invariant measure. Such a measure always exists if the chain is ergodic. In this paper, we continue the study of the asymptotic properties of π([x,∞)) as x → ∞ for the invariant measure π, which was started in [A. A. Borovkov, Stochastic Processes in Queue...

We give an overview of the quantum ergodicity result. 1. Quantum ergodicity in the physical space 1.1. Concentration of eigenfunctions. First, let us consider the case when M ⊂ R is a bounded domain with piecewise C∞ boundary and we take the operator ∆ = −∂ x1 − ∂ 2 x2 . We study the Dirichlet eigenvalues λ0 < λ1 ≤ λ2 ≤ . . . (with multiplicities taken into account) and the corresponding L norm...