The ergodic decomposition of asymptotically mean stationary random sources

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Hammersley’s Process with Sources and Sinks by Eric Cator

We show that, for a stationary version of Hammersley’s process, with Poisson “sources” on the positive x-axis, and Poisson “sinks” on the positive y-axis, an isolated second-class particle, located at the origin at time zero, moves asymptotically, with probability 1, along the characteristic of a conservation equation for Hammersley’s process. This allows us to show that Hammersley’s process wi...

Hammersley’s process with sources and sinks

We show that, for a stationary version of Hammersley’s process, with Poisson “sources” on the positive x-axis, and Poisson “sinks” on the positive y-axis, an isolated second class particle, located at the origin at time zero, moves asymptotically, with probability one, along the characteristic of a conservation equation for Hammersley’s process. This allows us to show that Hammersley’s process ...

Source Codes as Random Number Generators

A random number generator generates fair coin flips by processing deterministically an arbitrary source of nonideal randomness. An optimal random number generator generates asymptotically fair coin flips from a stationary ergodic source at a rate of bits per source symbol equal to the entropy rate of the source. Since optimal noiseless data compression codes produce incompressible outputs, it i...

Optimal encoding of non-stationary sources

The usual assumption for proofs of the optimality of lossless encoding is a stationary ergodic source. Dynamic sources with non-stationary probability distributions occur in many practical situations where the data source is formed from a composition of distinct sources, for example, a document with multiple authors, a multimedia document, or the composition of distinct packets sent over a comm...