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math-ph2025
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…
math-ph2025
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…
math-ph2025
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…