Probability Seminar

Terrence GeorgeBrown University
Arctic curves for groves

Monday, February 3, 2020 - 4:00pm
Malott 406

The limit shape phenomenon is a "law of large numbers'' for
random surfaces: the random surface looks macroscopically like the
"average surface". The first result of this kind was the celebrated
arctic circle theorem for domino tilings of the aztec diamond. The
limit shape has macroscopic regions with different qualitative
behavior, and the arctic curve is the boundary separating these
regions. The work of Kenyon, Okounkov, Sheffield and others has shown
that periodic lattices with non-trivial Newton polygons lead to rich
arctic curves with many frozen and gaseous regions. Groves are another
model, closely related to spanning trees, that exhibits an arctic
circle theorem, due to Petersen and Speyer. We compute arctic curves
for groves with non-trivial Newton polygons, and provide a geometric
description of asymptotic edge probabilities.