Simple exclusion process
introduction
- Heisenberg spin chain model
- can be viewed as a exclusion process (time evolution)
Bethe Ansatz and Exclusion Processes http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=39328&date=2011-02-01
Stochastic growth models in the plane
For aimple case, consider a graph of a random height function h.
Consider the rescaling
h^{\epsion}(x,t)=\epsilon h(\frac{x}{\epsilon},\frac{t}{\epsilon})
Then we expect to have
After some scaling argument, one may use KPZ equation to justify \epsilon^{2/3} as the order og the fluctuations of the above problem. But what is the law of the random \eta ?
Perhaps we can locate an example for which we can find exact formula for h as a result a formula for \eta. So for we have two examples that are "exactly solvable"
These examples are
Hammersley-Aldous-Diaconis (HAD) process and simple exclusion processes.
For the latter a trick known on Bethe ansatz is used to find very explicit formulas for various quantities of interest.
exclusion process
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history
encyclopedia
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://eom.springer.de
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
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- http://pythagoras0.springnote.com/
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- http://dx.doi.org/
question and answers(Math Overflow)
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experts on the field