Friday, April 16, 2010

Wigner's Random Matrix Theory and Human Behavior

My question: "Does Wigner's Random Matrix Theory apply to human behavioral driven systems?

If so, it may provide an unique analysis tool applicable to everything from terrorist communications to mental health treatment to network communication phenomena.


In a paper from 2006, Percy Deift of New York University showed how random matrix theory applies to the mathematics of certain games of solitaire, to the way buses clump together in cities, and the path traced by molecules bouncing around in a gas.

While "bus clumping" depends upon a wide variety of factors (like the physical systems originally targeted by this technique), it also depends upon human behavior. If there is an underlying physical system responding only to physical properties with an imposed human behavioral driving force and the composite system still follows the random matrix principles then only one of two conclusions can be drawn:
1. The physical characteristics of the system swamp the human behavioral drivers
2. The human behavioral drivers also follow the random matrix principles. Or at least the sum of the two systems does.
The latter conclusion (2) assumes that two interacting systems following random matrix principles also follows random matrix principles. I believe this can be shown by taking any complex system following random matrix principles and breaking it into subsystems. If arbitrary subsystems also follow the random matrix principles the the assertion is supported, if not proven.

Further investigation of human behavioral driven systems should be undertaken to ascertain if Wigner's Random Matrix Theory applies.