AN ARCTIC CIRCLE THEOREM FOR GROVES

• Main Authors: T. Kyle, Petersen, David Speyer
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: Arctic
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.108.8618; http://jamespropp.org/reach/Petersen/GROVE2.pdf

Abstract. In [4], Jockusch, Propp, and Shor proved a theorem descibing 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 Carrol and Speyer [1] as combinatorial interpretations for Laurent polynomials given by the cube recurrence, groves have observable frozen regions which we describe precisely here via asymptotic analysis of generating functions borrowed from Pemantle [6]. 1.