I would really appreciate if someone could explain.

What does a correlation function like a density-density correlation function $$C_{nn}(\vec x_1, \vec x_2)= \langle n(\vec x_1) n(\vec x_2)\rangle$$ measure, or what does it mean as a function? By this i don't mean what the interpretation of the result is but what does it do mathematically?

And even more important how does it do this. If someone could explain this in general terms general functions of randomly variables it would be very helpfull.

I know about this question but none of the answeres really describes what generally a correlation function signifies or how it does this mathematically. But this is exactly what i need to know. Shurely there must be a way to proove or at least understand this completely theoretically.

I know that the correlation is defined as covariance function normalized as in wikipedia. The normalization seemes to always be missing in physics. Is this because we just use normalized random variables?

I would really appreciate if someone could explain.

What does a correlation function like a density-density correlation function $$C_{nn}(\vec x_1, \vec x_2)= \langle n(\vec x_1) n(\vec x_2)\rangle$$ measure, or what does it mean as a function? By this i don't mean what the interpretation of the result is but what does it do mathematically?

And even more important how does it do this. If someone could explain this in general terms general functions of randomly variables it would be very helpfull.

I know about this question but none of the answeres really describes what generally a correlation function signifies or how it does this mathematically. But this is exactly what i need to know. Shurely there must be a way to proove or at least understand this completely theoretically.

I know that the correlation is defined as covariance function normalized as in wikipedia. The normalization seemes to always be missing in physics. Is this because we just use normalized random variables?

I would really appreciate if someone could explain.

What does a correlation function like a density-density correlation function $$C_{nn}(\vec x_1, \vec x_2)= \langle n(\vec x_1) n(\vec x_2)\rangle$$ measure, or what does it mean as a function.

And even more important how does it do this. If someone could explain this in general terms general functions of randomly variables it would be very helpfull.

I know about this question but none of the answeres really describes what generally a correlation function signifies or how it does this mathematically. But this is exactly what i need to know.

I would really appreciate if someone could explain.

What does a correlation function like a density-density correlation function $$C_{nn}(\vec x_1, \vec x_2)= \langle n(\vec x_1) n(\vec x_2)\rangle$$ measure, or what does it mean as a function? By this i don't mean what the interpretation of the result is but what does it do mathematically?

And even more important how does it do this. If someone could explain this in general terms general functions of randomly variables it would be very helpfull.

I know about this question but none of the answeres really describes what generally a correlation function signifies or how it does this mathematically. But this is exactly what i need to know. Shurely there must be a way to proove or at least understand this completely theoretically.

I know that the correlation is defined as covariance function normalized as in wikipedia. The normalization seemes to always be missing in physics. Is this because we just use normalized random variables?