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Probability Seminar presents "Maximum height of low-temperature 3D Ising interfaces"

Topic: 
Maximum height of low-temperature 3D Ising interfaces
Monday, September 30, 2019 - 4:00pm
Venue: 
Sequoia Hall Room 200
Speaker: 
Reza Gheissari (UC Berkeley)
Abstract / Description: 

Consider the random surface given by the interface separating the plus and minus phases in a low-temperature Ising model in dimensions d ≥ 3. Dobrushin (1972) famously showed that in cubes of side-length n the horizontal interface is rigid, typically exhibiting orderone height fluctuations. We study the large deviations of this interface and obtain a shape theorem for its pillar, conditionally on it reaching an atypically large height. We use this to analyze the law of the maximum height of the interface, Mn: we prove that for every β large, Mn/ log n → cβ in probability, and (Mn−E[Mn])n forms a tight sequence. Moreover, even though the centered sequence does not converge, all its subsequential limits satisfy uniform Gumbel tail bounds. 

 

This is joint work with Eyal Lubetzky.