Difference between revisions of "Ergodic Theory"
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| − | '''Ergodic Theory''' is the [[mathematical]] theory of well-behaved [[random]]ness. The [[random variable]]s can occur [[discrete]]ly or [[continuous]]ly, but the total [[probability]] over the time period is always 1 (so by the end of the time period, the [[random event]] will surely have | + | '''Ergodic Theory''' is the [[mathematical]] theory of well-behaved [[random]]ness. The [[random variable]]s can occur [[discrete]]ly or [[continuous]]ly, but the total [[probability]] over the time period is always 1 (so by the end of the time period, the [[random event]] will surely have occurred. The [[probability distribution]] takes extreme values over the class of shift invariant processes. |
| − | The first serious study of ergodic theory was performed by [[Ludwig Boltzmann]], who also coined the term. His thesis was to justify the use of [[equilibria]] to study [[ | + | The first serious study of ergodic theory was performed by [[Ludwig Boltzmann]], who also coined the term. His thesis was to justify the use of [[equilibria]] to study [[mechanics]] in a probabilistic model. [[John von Neumann]] and [[George David Birkhoff]] are other seminal contributors to the field. |
[[category:mathematics]] | [[category:mathematics]] | ||
Revision as of 16:56, November 8, 2008
Ergodic Theory is the mathematical theory of well-behaved randomness. The random variables can occur discretely or continuously, but the total probability over the time period is always 1 (so by the end of the time period, the random event will surely have occurred. The probability distribution takes extreme values over the class of shift invariant processes.
The first serious study of ergodic theory was performed by Ludwig Boltzmann, who also coined the term. His thesis was to justify the use of equilibria to study mechanics in a probabilistic model. John von Neumann and George David Birkhoff are other seminal contributors to the field.