# √2N

October 28, 2014 12:59 PM Subscribe

At the Far Ends of a New Universal Law

The law appeared in full form two decades later, when the mathematicians Craig Tracy and Harold Widom proved that the critical point in the kind of model May used was the peak of a statistical distribution. Then, in 1999, Jinho Baik, Percy Deift and Kurt Johansson discovered that the same statistical distribution also describes variations in sequences of shuffled integers — a completely unrelated mathematical abstraction. Soon the distribution appeared in models of the wriggling perimeter of a bacterial colony and other kinds of random growth. Before long, it was showing up all over physics and mathematics. “The big question was why,” said Satya Majumdar, a statistical physicist at the University of Paris-Sud. “Why does it pop up everywhere?”

Turtles man. All the way down

posted by Windopaene at 2:21 PM on October 28, 2014 [1 favorite]

posted by Windopaene at 2:21 PM on October 28, 2014 [1 favorite]

I'm sure there will be an exciting new financial product based on this idea in 5...4...3...

posted by marienbad at 2:51 PM on October 28, 2014 [3 favorites]

posted by marienbad at 2:51 PM on October 28, 2014 [3 favorites]

See, kids, when the Gaussian Distribution and the bifurcation fractal love each other very much...

posted by localroger at 3:34 PM on October 28, 2014 [2 favorites]

posted by localroger at 3:34 PM on October 28, 2014 [2 favorites]

I do not understand much of this--but I love it. Thanks heavens another universal distribution to give me some sense of order and predictability.

posted by rmhsinc at 4:00 PM on October 28, 2014 [2 favorites]

posted by rmhsinc at 4:00 PM on October 28, 2014 [2 favorites]

It's not a coincidence that the photo of Tracey & Widom is at Oberwolfach.

posted by zamboni at 4:14 PM on October 28, 2014

posted by zamboni at 4:14 PM on October 28, 2014

One more bit of evidence that the idea of equalibrium in "the market" is a fantasy.

posted by carping demon at 4:29 PM on October 28, 2014 [1 favorite]

posted by carping demon at 4:29 PM on October 28, 2014 [1 favorite]

Thanks for posting this. I look forward to digging in to it.

posted by benito.strauss at 5:21 PM on October 28, 2014

posted by benito.strauss at 5:21 PM on October 28, 2014

I'm not understanding the phase transition part - sure, a plot of energy vs. temperature will be lopsided. But, x axis is temperature, how does this relate to N, the "number of variables"? And what is the number of variables for the stock market? Seems like they are ascribing this function to every lopsided distribution.

posted by 445supermag at 9:15 PM on October 28, 2014

posted by 445supermag at 9:15 PM on October 28, 2014

445supermag:

I thought the population and graph examples were telling: as you have more edges in a graph, there are more ways for vertices to interact with one another, and above some critical density, the overall behaviour of the system changes.

For the question of over-application, the places they're seeing it come up are mostly pure math or mathematical models of things like the stock market. You build the model, and then (having set up the game) are in good position to observe the resulting distribution in much finer detail than you could with actual data. This makes it possible to nail down the distribution as the TW distribution. The surprise was that this distribution arose from a wide variety of models, across many disciplines.

It's a fantastic article!

posted by kaibutsu at 1:24 AM on October 29, 2014 [1 favorite]

I thought the population and graph examples were telling: as you have more edges in a graph, there are more ways for vertices to interact with one another, and above some critical density, the overall behaviour of the system changes.

For the question of over-application, the places they're seeing it come up are mostly pure math or mathematical models of things like the stock market. You build the model, and then (having set up the game) are in good position to observe the resulting distribution in much finer detail than you could with actual data. This makes it possible to nail down the distribution as the TW distribution. The surprise was that this distribution arose from a wide variety of models, across many disciplines.

It's a fantastic article!

posted by kaibutsu at 1:24 AM on October 29, 2014 [1 favorite]

The matrix representation of something has an eigenvalue that represents some property of interest? Shocked, I'm just shocked.

posted by bdc34 at 6:51 AM on October 29, 2014

posted by bdc34 at 6:51 AM on October 29, 2014

*The matrix representation of something has an eigenvalue that represents some property of interest? Shocked, I'm just shocked.*

It's depressing that not only do I not understand the article, I don't even understand the snark about the article.

posted by rodii at 7:52 AM on October 29, 2014 [7 favorites]

The phase transition part is indeed sloppily described*, but the point is that while the boiling of water is an example of a first-order phase transition, this distribution apparently resembles a third-order transition.

*The first derivative is described as having a peak, but it in fact flat goes to infinity (for a first-order transition). This is coupled to the fact that while you're boiling water, more heat doesn't increase the temperature---it just increases the boiling rate. In other words, liquid water has infinite heat capacity at 100°C.

posted by Mapes at 9:15 AM on October 29, 2014

*The first derivative is described as having a peak, but it in fact flat goes to infinity (for a first-order transition). This is coupled to the fact that while you're boiling water, more heat doesn't increase the temperature---it just increases the boiling rate. In other words, liquid water has infinite heat capacity at 100°C.

posted by Mapes at 9:15 AM on October 29, 2014

That Wikipedia article talks about third-order phase transitions as if they're some rare beast, while the FPP article makes it seem like they're everywhere. Am I mis-reading them, or is there actual a clash of views there?

posted by benito.strauss at 8:03 PM on October 29, 2014

posted by benito.strauss at 8:03 PM on October 29, 2014

Rare in physical materials, not so rare in models of abstract systems, perhaps.

posted by Mapes at 7:27 AM on October 30, 2014 [1 favorite]

posted by Mapes at 7:27 AM on October 30, 2014 [1 favorite]

>

I think the shock was that random matrices' eigenvalues, as a whole, form the TW-distribution.

posted by Monochrome at 12:07 PM on October 31, 2014 [1 favorite]

*The matrix representation of something has an eigenvalue that represents some property of interest?*I think the shock was that random matrices' eigenvalues, as a whole, form the TW-distribution.

posted by Monochrome at 12:07 PM on October 31, 2014 [1 favorite]

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posted by CrowGoat at 1:51 PM on October 28, 2014 [1 favorite]