EUDML

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Rigidity of planar tilings (Erratum).

Richard Kenyon — 1993

Inventiones mathematicae

Pavages autosimilaires à similitudes

Richard Kenyon

Séminaire de théorie spectrale et géométrie

Rigidity of planar tilings.

Richard Kenyon — 1992

Inventiones mathematicae

Inflationary tilings with a similarity structure.

Richard Kenyon — 1994

Commentarii mathematici Helvetici

Tilings of convex polygons

Richard Kenyon — 1997

Annales de l'institut Fourier

Call a polygon rational if every pair of side lengths has rational ratio. We show that a convex polygon can be tiled with rational polygons if and only if it is itself rational. Furthermore we give a necessary condition for an arbitrary polygon to be tileable with rational polygons: we associate to any polygon $P$ a quadratic form $q (P)$ , which must be positive semidefinite if $P$ is tileable with rational polygons. The above results also hold replacing the rationality...

Local statistics of lattice dimers

Richard Kenyon — 1997

Annales de l'I.H.P. Probabilités et statistiques

Intersecting random translates of invariant Cantor sets.

Richard Kenyon; Yuval Peres — 1991

Inventiones mathematicae

Dimers and cluster integrable systems

Alexander B. Goncharov; Richard Kenyon — 2013

Annales scientifiques de l'École Normale Supérieure

We show that the dimer model on a bipartite graph $Γ$ on a torus gives rise to a quantum integrable system of special type, which we call a. The phase space of the classical system contains, as an open dense subset, the moduli space $Ł_{Γ}$ of line bundles with connections on the graph $Γ$ . The sum of Hamiltonians is essentially the partition function of the dimer model. We say that two such graphs $Γ_{1}$ and $Γ_{2}$ areif the Newton polygons of the corresponding partition functions coincide up to translation. We define...