Ergodic states in a non commutative ergodic theory

Ergodic theorem, ergodic theory, and statistical mechanics.

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 simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundam...

Ergodic Theory

Ergodic theory involves the study of transformations on measure spaces. Interchanging the words “measurable function” and “probability density function” translates many results from real analysis to results in probability theory. Ergodic theory is no exception. Ergodic theory has fundamental applications in probability theory, starting from areas that are very well understood, such as finite st...

Non-Archimedean Ergodic Theory and Pseudorandom Generators

The paper develops techniques in order to construct computer programs, pseudorandom number generators (PRNG), that produce uniformly distributed sequences. The paper exploits an approach that treats standard processor instructions (arithmetic and bitwise logical ones) as continuous functions on the space of 2-adic integers. Within this approach, a PRNG is considered as a dynamical system and is...

Credal and pignistic reasoning in ergodic and non-ergodic texts

This paper discusses the difference between ergodic and non-ergodic texts by considering the different levels of reasoning required of an agent in each case. The difference indentified between such texts is based on the distinction between credal and pignistic reasoning in the transferable belief model. It is argued that non-ergodic texts require an active agent to reason about the state of the...

Introduction to Ergodic Theory