Ergodic and non-ergodic clustering of inertial particles

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...

Ergodic Properties of a Model for Turbulent Dispersion of Inertial Particles

We study a simple stochastic differential equation that models the dispersion of close heavy particles moving in a turbulent flow. In one and two dimensions, the model is closely related to the one-dimensional stationary Schrödinger equation in a random δ-correlated potential. The ergodic properties of the dispersion process are investigated by proving that its generator is hypoelliptic and usi...

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 Optimization for Non - Compactdynamical

An Application of Random Matrix Theory: Asymptotic Capacity of Ergodic and Non-ergodic Multiantenna Channels

Random matrices have fascinated mathematicians and physicists since they were first introduced in mathematical statistics by Wishart in 1928. The landmark contributions of Wishart, Wigner and later Marc̆enko-Pastur (in 1967) were motivated to a large extent by practical problems. Nowadays, random matrices find applications in fields as diverse as the Riemann hypothesis, stochastic differential e...