Student Probability Seminar

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Maximum of 3D Ising interfaces

Speaker: Joe Chen, CIMS

Location: Warren Weaver Hall 1314

Date: Monday, February 27, 2023, 1:15 p.m.

Synopsis:

Abstract: In interface models, it is useful to know the large deviation rate of the height of the interface above a fixed point, as this is the starting point from which many other results can be deduced, such as a more precise estimate for the maximum of the interface. These more precise details of the interface are determined by the balance of energy and entropy in the model – the “typical” interface should have both a relatively high probability of occurring (energy) and many possible ways for the interface to look in the way we expect it to (entropy). I will explain how the tool of “map arguments” is a very effective way to turn intuition from balancing energy and entropy into rigorous proofs, and how the desired large deviation rate follows once we establish such arguments.