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SUMMARY:The oriented swap process -  Dan Romik (Hebrew University)
DTSTART:20081007T130000Z
DTEND:20081007T140000Z
UID:TALK14293@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:The oriented swap process is a random walk on the symmetric gr
 oup of\norder N. Starting from the identity permutation\, at each step an\
 nadjacent swap is chosen uniformly and applied to the current\npermutation
 \, but only if it increases the number of inversions.\nEventually the walk
  terminates when it reaches the permutation with\nmaximal number of invers
 ions. In recent work with Omer Angel and\nAlexander Holroyd\, we analyzed 
 the asymptotic behavior of the oriented\nswap process when N tends to infi
 nity using the theory of totally\nasymmetric exclusion processes\, derivin
 g formulas for the limiting\ntrajectories of individual numbers ("particle
 s") in the permutation\nand for the flow of particles en masse. An interes
 ting connection to\nrandom matrix theory also makes an appearance. I will 
 explain these\nresults and show computer simulations.\n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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