Probabilistic limit shapes and harmonic functions

Istvan Prause (University of Eastern Finland)

05-Oct-2021, 13:00-14:00 (2 years ago)

Abstract: Limit shapes are surfaces in $\mathbb{R^3}$ which arise in the scaling limit of discrete random surfaces associated to various probability models such as domino tilings, random Young tableaux or the 5-vertex model. The limit surface is a minimiser of a gradient variational problem with a surface tension which encodes the local entropy of the model. I'll show that in an intrinsic complex variable these limit shapes can all be parametrised by harmonic functions across a variety of models. Some new features beyond determinantal settings will be discussed. The talk is based on joint works with Rick Kenyon.

complex variablesdynamical systems

Audience: researchers in the topic


CAvid: Complex Analysis video seminar

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Organizer: Rod Halburd*
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