In Mysterious Pattern, Math and Nature Converge

Is it really that strange that random matrix theory models so many things though? Matrices without stochasticity can already model so many things in nature. And the reason for that is much more because they are a really well studied area of math, rather than because of some deep mysterious thing about nature. (It's much more about that being the conventional tool that physicists learn in school.) Take some really well used technique (matrix theory) and add another property (randomness) and is it really that strange that the result (random matrix theory) explains a larger set of phenomenon than what was explained by each piece individually?

Here is an approachable article that puts the subject in more perspective: https://terrytao.wordpress.com/2010/09/14/a-second-draft-of-...

And here's journal paper that gives some examples outside of physics:

http://journals.plos.org/plosone/article?id=10.1371/journal....

This made me think of the Central Limit Theorem. (If 'non-contrived' independent observations with random variability are summed and normalized, they end up exhibiting the standard Gaussian "bell curve".) All kinds of natural "real world" phenomena end up neatly obeying a function that seems odd:

f(x) = K / sqrt(exp(x*x))

(The above characterization assumes N(0,1), and re-arranges terms a slight amount to highlight the interesting nature of the function.)

This article is (2013). Same magazine posted another article in 2014 that provided a different look at the same broad topic:

https://www.quantamagazine.org/beyond-the-bell-curve-a-new-u...

Related: Computation at the edge of Chaos (Langton): http://www.romanpoet.org/223/langton.edgeofchaos.pdf

The fine balance between chaos and order in computational terms.

Is this less-dramatically stated as a particular non-Gaussian PDF (prob dist func)?