Birkhoff's Ergodic Theorem -- from Wolfram MathWorld
Ergodic theory
Definition of Ergodic Hypothesis
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What is the ergodic hypothesis? (Stat. Mech. #4)
The Ergodic hypothesis: Intro to Ergodicity
What is ergodicity?
Ergodic theory 1
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Ergodic hypothesis
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Ergodicity
In the social sciences, the ergodic hypothesis corresponds to the assumption that individuals are representative of groups, and vice-versa, that group averages can adequately characterize what might be seen in an individual. This appears to not be the case: group level data often gives a poor indication of …
Ergodic theory
• Birkhoff, George David (1931), "Proof of the ergodic theorem", Proc. Natl. Acad. Sci. USA, vol. 17, no. 12, pp. 656–660, Bibcode:1931PNAS...17..656B, doi:10.1073/pnas.17.12.656, PMC 1076138, PMID 16577406.• Birkhoff, George David (1942), "What is the ergodic theorem?", Amer. Math. Monthly, vol. 49, no. 4, pp. 222–226, doi:10.2307/2303229, JSTOR 2303229.
Lecture Notes on Ergodic Theory
The Ergodic Hypothesis: For certain invariant measures µ, many functions f : X → R, and many states x = (q,p), the time average lim T→∞ 1 T R T 0 f(T t(x))dt exists, and equals the space …
Foundations of Ergodic Theory
Foundations of Ergodic Theory. one- or two-semester courses. The authors’ clear and fluent exposition helps the reader to grasp quickly the most important ideas of the theory, and their …
Notes on Ergodic Theory by Jeff Steif
ergodic hypothesis and is one of the origins of ergodic theory. Ergodic theory impinges on many areas of mathematics- most notably, probability theory and dynamical systems as well …
Modern Ergodic Theory: From a Physics Hypothesis to a …
Ergodic theory emerged as a statistical mechanics hypothesis and has quickly reached into a mature and influential mathematical theory. Beginning with a brief historical …
Ergodic Theory (Lecture Notes)
Ergodic theory lies in somewhere among measure theory, analysis, proba- bility, dynamical systems, and di⁄erential equations and can be motivated from many di⁄erent angles.
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In the social sciences, the ergodic hypothesis corresponds to the assumption that individuals are representative of groups, and vice-versa, that group averages can adequately characterize what might be seen in an individual. This appears to not be the case: group level data often gives a poor indication of …
• Birkhoff, George David (1931), "Proof of the ergodic theorem", Proc. Natl. Acad. Sci. USA, vol. 17, no. 12, pp. 656–660, Bibcode:1931PNAS...17..656B, doi:10.1073/pnas.17.12.656, PMC 1076138, PMID 16577406.• Birkhoff, George David (1942), "What is the ergodic theorem?", Amer. Math. Monthly, vol. 49, no. 4, pp. 222–226, doi:10.2307/2303229, JSTOR 2303229.
The Ergodic Hypothesis: For certain invariant measures µ, many functions f : X → R, and many states x = (q,p), the time average lim T→∞ 1 T R T 0 f(T t(x))dt exists, and equals the space …
Foundations of Ergodic Theory. one- or two-semester courses. The authors’ clear and fluent exposition helps the reader to grasp quickly the most important ideas of the theory, and their …
ergodic hypothesis and is one of the origins of ergodic theory. Ergodic theory impinges on many areas of mathematics- most notably, probability theory and dynamical systems as well …
Ergodic theory emerged as a statistical mechanics hypothesis and has quickly reached into a mature and influential mathematical theory. Beginning with a brief historical …
Ergodic theory lies in somewhere among measure theory, analysis, proba- bility, dynamical systems, and di⁄erential equations and can be motivated from many di⁄erent angles.