6 papers
Dimer models on astroidal zig-zag graphs
Tomas Berggren, Alexei Borodin, Terrence George
On a finite weighted graph, the dimer model is a probability measure on its dimer covers, that assigns to any cover a probability proportional to the product of the weights of its…
Marked GUE-corners process in doubly periodic dimer models
Tomas Berggren, Nedialko Bradinoff
We study a family of periodically weighted Aztec diamond dimer models near their turning points. We establish that, asymptotically, as , their fluctuations ther…
Perfect t-embeddings of doubly periodic Aztec diamonds
Tomas Berggren, Matthew Nicoletti, Marianna Russkikh
We study the large-scale geometry of t-surfaces -- pairs of perfect t-embeddings and their associated origami maps -- arising from dimer models on Aztec diamonds with periodic edge…
Perfect t-embeddings and the octahedron equation of the two-periodic Aztec diamond
Tomas Berggren, Marianna Russkikh
This paper explores the connection between perfect t-embeddings and the octahedron equation in the setting of the two-periodic Aztec diamond. In particular, we show that the positi…
Gaussian Free Field and Discrete Gaussians in Periodic Dimer Models
Tomas Berggren, Matthew Nicoletti
We analyze height fluctuations in Aztec diamond dimer models with nearly arbitrary periodic edge weights. We show that the centered height function approximates the sum of two inde…
Perfect t-embeddings and Lozenge Tilings
Tomas Berggren, Matthew Nicoletti, Marianna Russkikh
We construct perfect t-embeddings for regular hexagons of the hexagonal lattice, providing the first example, and hence proving existence, for graphs with an outer face of degree g…