A variational principle for domino tilings

  • Cohn H
  • Kenyon R
  • Propp J
  • 32


    Mendeley users who have this article in their library.
  • 94


    Citations of this article.


We formulate and prove a variational principle (in the sense of thermodynamics) for random domino tilings, or equivalently for the dimer model on a square grid. This principle states that a typical tiling of an arbitrary finite region can be described by a function that maximizes an entropy integral. We associate an entropy to every sort of local behavior domino tilings can exhibit, and prove that almost all tilings lie within epsilon (for an appropriate metric) of the unique entropy-maximizing solution. This gives a solution to the dimer problem with fully general boundary conditions, thereby resolving an issue first raised by Kasteleyn. Our methods also apply to dimer models on other grids and their associated tiling models, such as tilings of the plane by three orientations of unit lozenges.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Get full text


  • Henry Cohn

  • Richard Kenyon

  • James Propp

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free