Collective dynamics of chaotic chemical oscillators and the law of large numbers

Experiments on the nontrivial collective dynamics and phase synchronization of populations of nonidentical chaotic electrochemical oscillators are presented. Without added coupling no deviation from the law of large numbers is observed. Deviations do arise with weak global or short-range coupling; large, irregular, and periodic mean field oscillations occur along with (partial) phase synchronization.     

Strong law of large numbers in D-posets

The notion of an observable and a state on a D-poset have been introduced. In the present paper the independence of a sequence of observables is defined and the strong law of large numbers is proved.     

A note on q-weak law of large numbers

q-limit theorems for random variables are arising from non-extensive statistical mechanics. In this note we will prove q-weak law of large numbers using the notions of q-Fourier transform, q-independence, q-weak convergence.     

Concepts of convergence for a quantum law of large numbers

We introduce the notion of uniform convergence of an operator sequence relative to a state operator, and we compare it with the notion of almost everywhere convergence, introduced by Gudder. We show that a sequence (M_n) of mean-value operators

$\text{M}{}_{\mathrm{n}}\text{=}\text{1}\text{n}\text{∑n}\text{i=1}\text{1?…?A}{}_{\mathrm{i}}\text{?1?…,}$

defined on the infinite tensor product $\text{?}\text{i}\text{H}{}_{\mathrm{i}}$, converges relative uniformly to $\text{x}\text{1}$ if and only if it converges almost everywhere to $\text{x}\text{1}$.