4 ms·

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

115 points by dedalus 11y ago

photoJ 11y ago
Sadly, Leo P. Kadanoff, quoted in the article just passed away.
chollida1 11y ago
If anyone wants to dig into this further start here: https://www.math.ucdavis.edu/~tracy/talks/SITE7.pdf https://www.math.ucdavis.edu/~tracy/talks/SITE7.pdf I find it to be a very approachable paper.
kordless 11y ago
I immediately thought of this: http://www.enterprisetech.com/2014/05/22/cisco-ceo-predicts-brutal-brutal-consolidation/ http://www.enterprisetech.com/2014/05/22/cisco-ceo-predicts-...
mckoss 11y ago
"Suitably scaled, its summit sits at a telltale value: √2N" Doesn't this statement apply the any function with a maximum?
- rcthompson 11y ago
  "Suitably" doesn't mean "arbitrarily". In this case it probably means something like "relative to the number of variables, N".
paulpauper 11y ago
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
- kurlberg 11y ago
  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.
  - helmett 11y ago
    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.
    - gaze 11y ago
      Yeah but certain characteristic functions popping up in seemingly unrelated places is a BIG deal.
deepnet 11y ago
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 http://arxiv.org/abs/1509.04516

115 points by dedalus 11y ago

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

If anyone wants to dig into this further start here: https://www.math.ucdavis.edu/~tracy/talks/SITE7.pdf https://www.math.ucdavis.edu/~tracy/talks/SITE7.pdf I find it to be a very approachable paper.

kordless 11y ago

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

mckoss 11y ago

"Suitably scaled, its summit sits at a telltale value: √2N" Doesn't this statement apply the any function with a maximum?

rcthompson 11y ago
"Suitably" doesn't mean "arbitrarily". In this case it probably means something like "relative to the number of variables, N".

paulpauper 11y ago

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

kurlberg 11y ago
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.
- helmett 11y ago
  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.
  - gaze 11y ago
    Yeah but certain characteristic functions popping up in seemingly unrelated places is a BIG deal.

deepnet 11y ago

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 http://arxiv.org/abs/1509.04516