Talk:Ergodic theory

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Hello. I've stubbed this page with a defn of "ergodic" and a hand-wavy statement of the ergodic theorem. There are links to ergodic theory and ergodic hypothesis. I don't know how we want to split things up. Should ergodic, ergodic theorem, and ergodic theory all get separate pages? Put 'em all on the same page? I guess at this point my inclination is to put them all together since there is little material so far. Happy editing, Wile E. Heresiarch 02:30, 19 Feb 2004 (UTC)

I think this page should be moved to ergodic theory. I don't like using an adjective as a page title. This should be a redirect page. Michael Hardy 22:33, 13 Mar 2004 (UTC)

I agree about the page title. I will put in a request for the ergodic theory redirect to be removed so that the ergodic page can move there. Wile E. Heresiarch 18:03, 15 Mar 2004 (UTC)

It would be really nice if someone could come up with a sentence to put in the first paragraph that would make sense to a typical undergraduate math major. (I'm not even gonna say "typical reader"!) Maybe that's just not possible given the topic? - dcljr 03:45, 20 Jul 2004 (UTC)

Hi, I went here to find something on ergodicity as in "ergodic Markov model", more precisely the stuff with stationary distributions -- on one hand, it takes a little thinking to match the abstract stuff here with the very constrained notions used for MMs (if you're vaguely familiar with them), on the other, the page on MMs just handwavingly refers to here. I think that MMs would be a fine illustrating example here, but I'm not familiar enough with ergodic theory to write up (or even think up) a good formulation - Yannick V.

[edit] Revised intro

My proposal for a more amenable and general statement:

Generally, an ergodic theorem refers to any statement about the existence of a mean value with respect to trajectories of a random process taken with respect to time. Intuitively it means that the mean of a random process is irrespective of it's starting point.

A subsection with ergodic theorem should be included.

Sounds good to me. linas 00:36, 16 December 2005 (UTC)

This is a somewhat pedantic point, but strictly speaking the equidistribution theorem is not a special case of the ergodic theorem: the equidistribution theorem gives pointwise convergence at every point, which is a stronger statement than the Lebesgue-a.e. convergence given by applying the Birkhoff theorem. 193.170.117.12 14:35, 10 May 2006 (UTC)

[edit] copyright violation?

The first two paragraphs copy verbatim the 3rd and 4th paragraphs of the linked article at http://news.softpedia.com/news/What-is-ergodicity-15686.shtml. Of course, the copy could have gone the other direction. It's not clear if this is small enough to be fair use, but it should certainly be credited.

Those paragraphs were added by OO0000OO on 26 March 2006. As of 11 April 2006 those paragraph are the user's sole contribution to the WP. I have removed the section, as Softpedia claims the material copyrighted. XaosBits 21:38, 11 April 2006 (UTC)