For more than a century scientists have relied on the “ergodic theorem” to explain diffusive processes such as the movement of molecules in a liquid. However, they had not been able to confirm ...

This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly ...

This is a preview. Log in through your library . Abstract One can explicitly construct unbounded functions having bounded mean oscillation (and in fact vanishing mean oscillation) with respect to any ...

Extracting the light trapped in a waveguide, or the opposite effect of trapping light in a thin region and guiding it perpendicular to its incident propagation direction, is essential for optimal ...

The study of ergodic breaking is instructive for market collapse and recovery in finance, brain epilepsy in neural networks, and early warning of critical leaps in complex systems. Rydberg atoms ...