Thursday, 14th February 2008, 4:00 pm

Mathematics Building, Lecture Hall 2

Dan Romik

(Hebrew University)

"The directed random walk on the permutahedron"

** Abstract: **In the symmetric group of order *N*, start from the identity permutation and
repeatedly choose a uniform random integer *0< k< N*, then apply to the
permutation the adjacent transposition *(k,k+1)* if the permutation that
results has more inversions than the current one. This is a finite random
walk that ends after exactly *N(N-1)/2* steps, when one reaches the
permutation *(N,N-1,...2,1)* with the maximal number of inversions. I will
describe a surprising analysis of the limiting behavior of this random
walk when *N* goes to infinity, using results from the theory of interacting
particle systems (prior knowledge of this theory will not be assumed).

The talk is based on joint work with Omer Angel and Alexander Holroyd.

Light refreshments will be served in the faculty lounge at 3:30.

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