So I have a question about power spectral densities and correlations of noise. I know that there is the Wiener–Khinchin theorem that can connect the two with a Fourier transform, and that a white noise process (flat power spectral density) has no correlations between the points; the correlation function is a delta function. But what if we now take a white noise process with a cutoff? Say it is white from 0 to 200 MHz, with some amplitude A, but after that it is 0

You can think of the cutoff as a fermi dirac type of cutoff if you will; it just goes from A to 0 very rapidly after 200 MHz. What kind of correlations does this noise have? It is no longer a delta function, but what is it

@ACuriousMind Does this look right?

@0celo7 I guess it is correct, but using Sard's theorem and not Seifert-van Kampen to prove this doesn't look "right" to me ;)

@ACuriousMind You damn algebraist

@ChrisWhite Nah, not the stuff about sports.

@ChrisWhite I knew about that thing.

@ACuriousMind Pls entertain me

I'm in a dark room waiting for spectroscopy measurements

And I'm using the wrong laser FML

can subgroups of an infinite cyclic group have finite order

my intuition says no

@Obliv no because it contains unity and then generates the full group

I think...

It's really sad watching the evolution of a crackpot.

He started out sound reasonable but slightly rude. Then more rude. Now his theory has a name, "Dynamic Dimensions Theory", and he's writing long rants about it.

@knzhou not to mention he asked nearly the same question earlier.

Iceland is about to beat England.

@Danu Hmm?

@danu I love how every single starter on iceland has last name ending in -son

I love Iceland

@0celo7 I don't know what you meant by unity. If you meant zero, then zero will not generate the whole group, because 0+0=0. If you meant one, well one isn't always in the group. For example, one is not in 3Z. The answer should be yes since the subgroup containing just the identity has finite size. If you exclude this case, then the answer should be no because any infinite cyclic group is isomorphic to Z and if n is in a subgroup of Z, then so must all of nZ, which has infinite size.

Can Tipler cylinder or Gott spacetimes even exist with a cosmic string

Cosmic strings don't really obey the Polyakov action

It's just an approximation

Wait

If they can be made in such a way

Then it would be doable to use as a source for a CTC spacetime in quantum gravity

STOP THE PRESSES