ergodicity उदाहरण वाक्य

When implementing the algorithm, we must ensure that " g " ( ?, ? ) is selected such that ergodicity is met.
The properties of ergodicity, weak mixing and strong mixing of a measure-preserving dynamical system can also be characterized by the average of observables.
These assumptions of ergodicity are well-motivated in classical mechanics as a result of dynamical hard sphere gas has been rigorously proven to be ergodic.
Under the assumption of point process ergodicity ( satisfied when using homogeneous Poisson processes ), the results for the typical user correspond to user averages.
This shows that some sort of mixing of energies, formally called " ergodicity ", is important for the law of equipartition to hold.

In a series of two papers ( one co-authored with Jean Bourgain ) he made major progress on Peter Sarnak's Arithmetic Quantum Unique Ergodicity conjecture.
Anantharaman was included for her work in " quantum chaos, dynamical systems and Schr�dinger equation, including a remarkable advance in the problem of quantum unique ergodicity ".
The validity of the continuum assumption may be verified by a theoretical analysis, in which either some clear periodicity is identified or statistical homogeneity and ergodicity of the microstructure exists.
If sufficiently strong nonlinear terms are present in the energy function, energy may be transferred between the normal modes, leading to ergodicity and rendering the law of equipartition valid.
Assuming that a particular system approaches all possible states over very long times ( quasi-ergodicity ), the resulting Monte Carlo dynamics realistically sample microscopic states that correspond to the given energy value.