Phase boundary fluctuation and growth models
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Tue, 18/05/2010 16:30 |
Alan Hammond (University of Oxford) |
Combinatorial Theory Seminar  |
SR2 |
| The Wulff droplet arises by conditioning a spin system in a dominant phase to have an excess of signs of opposite type. These gather together to form a droplet, with a macroscopic Wulff profile, a solution to an isoperimetric problem. I will discuss recent work proving that the phase boundary that delimits the signs of opposite type has a characteristic scale, both at the level of exponents and their logarithmic corrections. This behaviour is expected to be shared by a broad class of stochastic interface models in the Kardar-Parisi-Zhang class. Universal distributions such as Tracy-Widom arise in this class, for example, as the maximum behaviour of repulsive particle systems. time permitting, I will explain how probabilistic resampling ideas employed in spin systems may help to develop a qualitative understanding of the random mechanisms at work in the KPZ class. | |||