  In earlier work, Jockusch, Propp, and Shor proved a theorem describing the
limiting shape of the boundary between the uniformly tiled corners of a random
tiling of an Aztec diamond and the more unpredictable `temperate zone' in the
interior of the region. The so-called arctic circle theorem made precise a
phenomenon observed in random tilings of large Aztec diamonds.
  Here we examine a related combinatorial model called groves. Created by
Carroll and Speyer as combinatorial interpretations for Laurent polynomials
given by the cube recurrence, groves have observable frozen regions which we
describe precisely via asymptotic analysis of a generating function. Our
approach also provides another way to prove the arctic circle theorem for Aztec
diamonds.
