Mixing (mathematics)
In mathematics, mixing is an abstract concept originating from physics: the attempt to describe the irreversible thermodynamic process of mixing in the everyday world: mixing paint, mixing drinks, etc.
The concept appears in ergodic theory—the study of stochastic processes and measure-preserving dynamical systems. Several different definitions for mixing exist, including strong mixing, weak mixing and topological mixing, with the last not requiring a measure to be defined. Some of the different definitions of mixing can be arranged in a hierarchical order; thus, strong mixing implies weak mixing. Furthermore, weak mixing (and thus also strong mixing) implies ergodicity: that is, every system that is weakly mixing is also ergodic (and so one says that mixing is a "stronger" notion than ergodicity).
Read more about Mixing (mathematics): Mixing in Stochastic Processes, Mixing in Dynamical Systems, Topological Mixing, Generalizations
Famous quotes containing the word mixing:
“Give me Catholicism every time. Father Cheeryble with his thurible; Father Chatterjee with his liturgy. What fun they have with all their charades and conundrums! If it weren’t for the Christianity they insist on mixing in with it, I’d be converted tomorrow.”
—Aldous Huxley (1894–1963)