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A Curie-Weiss model of self-organized criticality

Where:  TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.
When:  20th of June 2017
Starttime  12:45

On Tuesday (20/06/2017), we have another interesting talk in our Probability and Statistics seminar series at TU Delft. All of you are very welcome.

Matthias Gorny (Université Paris-Sud)

When: Tuesday June 20th, 12:45 
Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.

A Curie-Weiss model of self-organized criticality

In their famous 1987 article, Per Bak, Chao Tang and Kurt Wiesenfeld showed that certain complex systems, composed of a large number of dynamically interacting elements, are naturally attracted by critical points, without any external intervention. This phenomenon, called self-organized criticality (SOC), can be observed empirically or simulated on a computer in various models. However the mathematical analysis of these models turns out to be extremely difficult. Even models whose definition seems simple, such as the models describing the dynamics of a sandpile, are not well understood mathematically. In my presentation, I will introduce a model of SOC which is built by modifying the generalized Ising Curie-Weiss model. I will present a fluctuation theorem which proves that this model indeed exhibits SOC: the sum $S_{n}$ of the random variables behaves as in the typical critical generalized Ising Curie-Weiss model, i.e., the fluctuations are of order $n^{3/4}$ and the limiting law is $C exp(-lambda x^{4}),dx$ where $C$ and $lambda$ are suitable positive constants. Finally I will introduce associated dynamic models of SOC.



 
More details here: http://goo.gl/TXD1Sw
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