Beyond the Bell Curve, a New Universal Law (2014) | Hacker News Reader

Beyond the Bell Curve, a New Universal Law (2014)

quantamagazine.org

115 pointsdedalus10 comments

If anyone wants to dig into this further start here:

https://www.math.ucdavis.edu/~tracy/talks/SITE7.pdf

I find it to be a very approachable paper.

Sadly, Leo P. Kadanoff, quoted in the article just passed away.

New paper by Majumdar & Schehr ( who discovered the E^-N^2 vs E^-N asymmetric tails to the Tracy-Widom Distribution in the OP ) looking for phase transitions in random walks.

"Random walk with random resetting to the maximum" by Majumdar, Sabhapandit, & Schehr

http://arxiv.org/abs/1509.04516

"Suitably scaled, its summit sits at a telltale value: √2N"

Doesn't this statement apply the any function with a maximum?

"Suitably" doesn't mean "arbitrarily". In this case it probably means something like "relative to the number of variables, N".

I immediately thought of this: http://www.enterprisetech.com/2014/05/22/cisco-ceo-predicts-...

there already exist methods to generate skewed distributions that are very similar to the ones shown in the article. not sure how this is new. Skewed distributions arise form a more general case of the normal distribution but with added parameters or the use of special functions

The main point is not about generating skewed distributions, it's about "universality" - the same distribution starts popping up in seemingly unrelated settings. E.g., (large) eigenvalues of random matrices is connected to the length of the longest increasing subsequence of permutations. In a sense it's the discovery of a new kind of central limit theorem.

As someone who has studied statistics in college, there is little original or novel about these finding. Any distribution can be reversed-engineered to find its characteristic function.

Yeah but certain characteristic functions popping up in seemingly unrelated places is a BIG deal.

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