5 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…
Kenyon's identities for the height function and compactified free field in the dimer model
Mikhail Basok
In his seminal paper published in 2000 Kenyon developed a method to study the height function of the planar dimer model via discrete complex analysis tools. The core of this method…
Nesting of double-dimer loops: local fluctuations and convergence to the nesting field of CLE(4)
Mikhail Basok, Konstantin Izyurov
We consider the double-dimer model in the upper-half plane discretized by the square lattice with mesh size . For each point in the upper half-plane, we consider the random…
Dimers on Riemann surfaces and compactified free field
Mikhail Basok
We consider the dimer model on a bipartite graph embedded into a locally flat Riemann surface with conical singularities and satisfying certain geometric conditions in the spirit o…