ergodic Synonyms
No Synonyms and anytonyms found
ergodic Meaning
ergodic (s)
positive recurrent aperiodic state of stochastic systems; tending in probability to a limiting form that is independent of the initial conditions
ergodic Sentence Examples
- In the realm of probability theory, ergodic processes exhibit a fundamental property known as ergodicity.
- Ergodicity, a pivotal concept in statistical mechanics, asserts that time averages and ensemble averages converge, providing a profound connection between macroscopic and microscopic perspectives.
- Ergodic systems, characterized by their remarkable property of interchangeability between time and ensemble averages, play a pivotal role in understanding the behavior of complex systems.
- The ergodic hypothesis, a cornerstone of statistical mechanics, provides a powerful tool for investigating the long-term behavior of systems with many degrees of freedom.
- Ergodic processes, ubiquitous in various fields, including finance, economics, and physics, exhibit statistical properties that are invariant under time shifts.
- Ergodic theory delves into the mathematical foundations of ergodicity and its implications for various dynamical systems.
- Ergodic Markov chains, a particular class of stochastic processes, possess the remarkable property that their long-term behavior is independent of the initial state.
- Mixing, a key aspect of ergodic theory, refers to the ability of a dynamical system to redistribute its initial conditions over time.
- Ergodic transformations, characterized by their ability to preserve measure, play a central role in the study of ergodic theory and dynamical systems.
- Ergodicity and mixing are fundamental concepts that underlie our understanding of the behavior of complex systems, from molecular dynamics to financial markets.
FAQs About the word ergodic
positive recurrent aperiodic state of stochastic systems; tending in probability to a limiting form that is independent of the initial conditions
No synonyms found.
No antonyms found.
In the realm of probability theory, ergodic processes exhibit a fundamental property known as ergodicity.
Ergodicity, a pivotal concept in statistical mechanics, asserts that time averages and ensemble averages converge, providing a profound connection between macroscopic and microscopic perspectives.
Ergodic systems, characterized by their remarkable property of interchangeability between time and ensemble averages, play a pivotal role in understanding the behavior of complex systems.
The ergodic hypothesis, a cornerstone of statistical mechanics, provides a powerful tool for investigating the long-term behavior of systems with many degrees of freedom.
