Weakly mixing but not mixing quasi-Markovian processes

Quasi Markovian behavior in mixing maps

We consider the time dependent probability distribution of a coarse grained observable Y whose evolution is governed by a discrete time map. If the map is mixing, the time dependent one-step transition probabilities converge in the long time limit to yield an ergodic stochastic matrix. The stationary distribution of this matrix is identical to the asymptotic distribution of Y under the exact dy...

Mixing Processes

The ocean’s effect on weather and climate is governed largely by processes occurring in the few tens of meters of water bordering the ocean surface. For example, water warmed at the surface on a sunny afternoon may remain available to warm the atmosphere that evening, or it may be mixed deeper into the ocean not to emerge for many years, depending on near-surface mixing processes. Local mixing ...

Upper Ocean Mixing Processes

stratiRed (vertical gradients of potential temperature, salinity and potential density, averaged horizontally or in time, are zero). The terminology is most precise in the case of a convectively forced boundary layer. Elsewhere, oceanographers use the term loosely to describe the region of the ocean that responds most directly to surface processes. Late in the day, following periods of strong h...

An extension which is relatively twofold mixing but not threefold mixing

We give an example of a dynamical system which is mixing relative to one of its factors, but for which relative mixing of order three does not hold. 1. Factors, extensions and relative mixing 1.1. Factors, extensions and Rokhlin cocycle. We are interested in dynamical systems (X,A , μ, T ), where T is an ergodic automorphism of the Lebesgue space (X,A , μ). We will often designate such a system...

Fronts and Mixing Processes