"Simple exclusion process"의 두 판 사이의 차이
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| − | After some scaling argument, one may use KPZ equation to justify \epsilon^{2/3} as the order og the | + | 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 ? |
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| + | 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" | ||
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| + | These examples are | ||
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| + | Hammersley-Aldous-Diaconis (HAD) process and simple exclusion processes. | ||
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| + | For the latter a trick known on Bethe ansatz is used to find very explicit formulas for various quantities of interest. | ||
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| + | <h5>exclusion process</h5> | ||
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| + | N | ||
2011년 2월 2일 (수) 09:48 판
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
N
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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articles
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
blogs
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- http://ncatlab.org/nlab/show/HomePage
experts on the field