22 citations · 44 across the 9 of their papers we have counts for
12 papers
T-embeddings as stationary measures on T-graphs
Mikhail Basok, Benoit Laslier, Marianna Russkikh
In this paper, we investigate the relation between t-embeddings and T-graphs associated with the same weighted planar bipartite graph. We prove that, given such a T-graph, the corr…
Harmonic functions on Tutte embeddings and linearized Monge-Ampère equation
Mikhail Basok, Dmitry Chelkak, Benoît Laslier +1
We prove convergence of solutions of Dirichlet problems and Green's functions on Tutte harmonic embeddings to those of the linearized Monge--Ampère equation . Mor…
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…
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…
Perfect t-embeddings of uniformly weighted Aztec diamonds and tower graphs
Tomas Berggren, Matthew Nicoletti, Marianna Russkikh
In this work we study a sequence of perfect t-embeddings of uniformly weighted Aztec diamonds. We show that these perfect t-embeddings can be used to prove convergence of gradients…
Bipartite dimer model: perfect t-embeddings and Lorentz-minimal surfaces
Dmitry Chelkak, Benoît Laslier, Marianna Russkikh
This is the second paper in the series devoted to the study of the dimer model on t-embeddings of planar bipartite graphs. We introduce the notion of perfect t-embeddings and assum…
Lozenge tilings and the Gaussian free field on a cylinder
Andrew Ahn, Marianna Russkikh, Roger Van Peski
We use the periodic Schur process, introduced in arXiv:math/0601019v1, to study the random height function of lozenge tilings (equivalently, dimers) on an infinite cylinder distrib…
Dimer model and holomorphic functions on t-embeddings of planar graphs
Dmitry Chelkak, Benoît Laslier, Marianna Russkikh
We introduce the framework of discrete holomorphic functions on t-embeddings of weighted bipartite planar graphs; t-embeddings also appeared under the name Coulomb gauges in a rece…
Dimers and Circle patterns
Richard Kenyon, Wai Yeung Lam, Sanjay Ramassamy +1
We establish a correspondence between the dimer model on a bipartite graph and a circle pattern with the combinatorics of that graph, which holds for graphs that are either planar…
Dominos in hedgehog domains
Marianna Russkikh
We introduce a new class of discrete approximations of planar domains that we call "hedgehog domains". In particular, this class of approximations contains two-step Aztec diamonds…
Dimers in piecewise Temperleyan domains
Marianna Russkikh
We study the large-scale behavior of the height function in the dimer model on the square lattice. Richard Kenyon has shown that the fluctuations of the height function on Temperle…