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Speaker: Joan Lind, UTK

Title: Convergence Via Discrete Modulus 

Abstract: Discrete modulus provides a useful framework for studying a variety of graph theoretic objects. In this talk, we will be interested in objects that approximate continuous counterparts. For instance, we show that there is a family of discrete paths that approximate the extremal curves for the (continuous) modulus of the curve family connecting two arcs in a Jordan domain. Moreover, the discrete paths carry a natural probability measure deriving from the theory of discrete modulus, and these measures converge to a natural measure on the set of extremal curves. One key ingredient is the convergence of certain discrete harmonic functions to continuous harmonic functions. As a second example, we will look at the convergence of Peano curves associated with certain random spanning trees. This is joint work with Nathan Albin and Pietro Poggi-Corradini.

Friday, October 29, 2021 at 3:35pm to 4:35pm

Ayres Hall, 405
1403 Circle Drive, Knoxville, TN 37996

Event Type

Lectures & Presentations



Contact Name

Ioannis Sgouralis

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