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DTSTART:20070311T020000
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DTSTAMP:20241201T151730
DTSTART;TZID=America/Detroit:20241203T170000
DTEND;TZID=America/Detroit:20241203T180000
SUMMARY:Workshop / Seminar:Student Analysis Seminar: Introduction to Random Lozenge Tilings
DESCRIPTION:Given a planar triangular lattice domain R\, one can ask how many lozenge tilings of R exist\, or if one even exists at all.  These questions can be answered by associating a tiling of R both with a height function defined on the lattice and with a perfect matching of its dual graph.  Upon introducing a probability measure on these tilings\, one finds that random height functions converge to a deterministic limit shape as the tile size decreases.  In this talk\, we will discuss how to compute this limit shape as the solution of a variational problem.  We will also introduce the Kenyon-Okounkov conjecture on convergence of fluctuations of centered height functions to the Gaussian free field\, a random generalized function on a region equipped with a certain complex structure.
UID:129527-21863543@events.umich.edu
URL:https://events.umich.edu/event/129527
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4096
CONTACT:
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