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Fully packed loops and the Razumov-Stroganov-Cantini-Sportiello theorem

Mathematical Physics & Probability

Speaker: Dan Romik, UC Davis
Location: 1147 MSB
Start time: Wed, Apr 13 2011, 4:10PM

The Razumov-Stroganov eigenvector is a probability vector whose coordinates are stationary probabilities for a random walk on the set of noncrossing matchings of 2n points arranged in a circle, where at each step of the walk two adjacent points in a randomly chosen position on the circle are matched with each other, with their previous discarded matches being also paired off with each other to create a new matching. In 2001, Razumov and Stroganov noticed empirically that (after some normalization) these probabilities can be interpreted as the cardinalities of sets of interesting combinatorial objects called fully packed loops (which are also known to be in bijection with alternating sign matrices). This fascinating discovery became known as the Razumov-Stroganov Conjecture, and was finally proved last year by Cantini and Sportiello. In this talk I will give a sketch of this beautiful and completely elementary proof.