Local statistics of lattice dimers

Local Statistics of Lattice Dimers

We show how to compute the probability of any given local configuration in a random tiling of the plane with dominos. That is, we explicitly compute the measures of cylinder sets for the measure of maximal entropy μ on the space of tilings of the plane with dominos. We construct a measure ν on the set of lozenge tilings of the plane, show that its entropy is the topological entropy, and compute...

Edge Effects on Local Statistics in Lattice Dimers: a Study of the Aztec Diamond (finite Case) by Harald Helfgott Thesis

Local Statistics of Lattice Points on the Sphere

A celebrated result of Legendre and Gauss determines which integers can be represented as a sum of three squares, and for those it is typically the case that there are many ways of doing so. These different representations give collections of points on the unit sphere, and a fundamental result, conjectured by Linnik, is that under a simple condition these become uniformly distributed on the sph...

Lattice Animals and Heaps of Dimers

Lattice animals and heaps of dimers