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Caltech/UCLA/USC Joint Analysis Seminar

Tuesday, May 31, 2022
2:30pm to 3:30pm
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Monotonicity theorems for integer-valued fields and delocalization in two-dimensions
Jacob Shapiro, Department of Physics, Princeton University,

Caltech, 310 Linde Hall

Integer-valued fields are restricted to take values in Z and usually their Gibbs factor depends only on the gradient of the field. When the Gibbs factor is such that the typical value of the gradients is much larger than 1 (the spacing of points in Z), the integer constraint becomes less relevant so the field behaves as if it were real-valued and "delocalizes". In 2D, this delocalization is associated with the Berezinskii–Kosterlitz–Thouless phase of the dual O(2) spin model. I will explain these notions for various models and present recent monotonicity theorems for fluctuations which are important to establish the delocalized phase.
Joint with: Michael Aizenman, Matan Harel and Ron Peled.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].