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

particles jumping from left ro right or from right ro left with given probabilityes p and q (p+q=1)

 

G(x,t) = probability (x(t)=x | x(0) is distrbuted according to g(x) )

 

 

 

 

 

history

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

related items

• Heisenberg spin chain model
• total positivity
• KPZ equation

 

 

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

 

• 2011년 books and articles
• http://library.nu/search?q=
• http://library.nu/search?q=

 

 

 

 

 

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)

• http://mathoverflow.net/search?q=
• http://mathoverflow.net/search?q=

 

 

blogs

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
    
  • http://blogsearch.google.com/blogsearch?q=
• http://ncatlab.org/nlab/show/HomePage

 

 

experts on the field

• http://arxiv.org/

 

 

links

• Detexify2 - LaTeX symbol classifier
• 수식표현 안내
• The On-Line Encyclopedia of Integer Sequences
• http://functions.wolfram.com/