Talk:Campbell's theorem (geometry)

The actual statement of the theorem is not given here. Can someone supply that? Michael Hardy (talk) 17:08, 2 July 2008 (UTC)

There are two Campbell's theorems that are being conflated here. One is the theorem of N.R. Campbell, from N.R. Campbell, Proc. Camb. Philos. Soc. v15 p117 1909 and N.R. Campbell, Proc. Camb. Philos. Soc. v15 p310 1909, which is about random impulses acting on a system. The other Campbell's theorem is from J.E. Campbell's 1926 book, A Course of Differential Geometry (Clarendon Press, Oxford) and is the one that both other names given and the bulk of the article refer to.

I'd be happy to fill in some stuff about the theorem of N.R. Campbell, but I don't hμave time right now, and I think these need to be separate articles since they're not related at all. --Hollow08 (talk) 03:50, 5 August 2008 (UTC)

NR Campbell theorem
N.R. Campbell's theorem (1909) on shot noise is as follows:

Consider a device that responds to an ideal impulse (a delta function) of charge q with a response R(t). The mean response to a random series of such impulses occurring at the mean rate μ is

R = μq ∫ F(t) dt

with fluctuations

(δR)2 = μ q2 ∫ F2(t) dt

Hopefully someone who knows more about this material can move this stub to a new page and expand on it. DrMicro (talk) 09:41, 6 August 2011 (UTC)

Two articles
I've created a second article page. There is now an article Campbell's theorem (geometry) and an article Campbell's theorem (probability), both linked from a disambiguation page Campbell's theorem. The new probability article is a stub, but references Kingman's book where a theorem and proof can be found. Gareth Jones (talk) 13:40, 1 March 2012 (UTC)