I’m guessing you used altitude for amplitude, but for power (angular) and phase, I’m at a loss (for the Earth map). ]]>

In general, I doubt the PhD-type physics people are primarily programmers, they are more on the ‘quant’ side doing modeling and extensive data analysis. Analyzing risk and the interaction of risk components across assets and asset classes on various time domains is one key area for highly quantitative people in the field. One of the short comings of the quants is that they are not as strong on intuition as they are with their other tools and thus they tend not to build the ability to apply intuition to the problems that they face.

I think that this was a problem for the guys at Long-Term Capital Management (Merton and Scholes, Nobels in 1997) especially because great early returns pushed them more and more into risky assets and then the hedge fund imploded in four months with the Asian and Russian crises, going bankrupt. Hard to model that the modest and even negative correlations under normal conditions get more and more positively correlated under extreme conditions. Most straight models can be very misleading for situations where there is not much data, and quants can get badly burned. [note: my background in economics; I am a neophyte in physics but I find it more interesting in retirement.]

]]>My understanding is that the assumption of Gaussianity in the CMB is reasonable, in the sense that it would be anyone’s first guess (with or without inflation) and no counter evidence has emerged from lensing etc. Thus, arguing from naturalness, it’s likely that the amplitudes of the peaks should indeed be interpreted the way they are, is that right? ]]>

1. Generate a Gaussian random field in the usual way.

2. Flip a coin, and multiply all the values in this map by 1000 if it comes up heads.

This process produces a map with random phases (after all, the phases after step 2 are the same as before), but the coefficients of the various harmonic modes are not independent, and the random process is not even approximately Gaussian.

As I’ve admitted, this example is silly, but it does show that there is no necessary logical connection between random phases and Gaussianity.

The reason this example yields non-Gaussianity is also the reason it’s silly: it involves strong (and implausible) dependence among the various modes. If the various modes are independent, then I agree that you get (approximate) Gaussianity.

But here’s the point: That last statement is true regardless of whether the phases are random. If you build your map out of many independent random variables, in such a way that many terms contribute significantly to each point in the map, then the central limit theorem will give you approximate Gaussianity, whether or not the phases are random.

So there is, as far as I am aware, precisely no logical connection between randomness of phases and Gaussianity.

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