Probability and Statistics Seminar—— Dimer model, uniform spanning tree and Gaussian free ﬁeld
报告人： 刘明昶 ( 清华大学|以诚为本·赢在信誉9001)
地点：Room 1114, Sciences Building No. 1
The dimer model is one of the simplest but also most intriguing models of statistical mechanics. It is typically studied through its height function, which turns the dimer model into a model of random surfaces. The main question is its large scale behaviour. A remarkable conjecture of Kenyon and Okunkov predicts that the large scale behaviour is in great generality described by the Gaussian free ﬁeld. This conjecture was proved by Kenyon in the case of Temperleyan boundary conditions. We generalized this result to the piecewise Temperleyan and simply connected domains. Our method is based on considering the spanning tree associated to this model via Temperley’s bijection. As a byproduct, we showed that the a pair of multiple SLE8 reduces to a more standard SLE8(ρ) conditional on the hitting point. This decomposition can also be generated to a more general setting–hypergeometric SLEs. This talk is based on a joint work with Nathana¨el Berestycki and an independent work.
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