Over the past 25 years, there has been an explosion of interest in the area of random tilings.
The first book devoted to the topic, this timely text describes the mathematical theory of …

Fractional Gaussian fields are scalar-valued random functions or generalized functions on
an $ n $-dimensional manifold $ M $, indexed by a parameter $ s $. They include white …

Domino tilings of the two-periodic Aztec diamond feature all of the three possible types of
phases of random tiling models. These phases are determined by the decay of correlations …

A characterisation of the Gaussian free field | Probability Theory and Related Fields Skip to
main content SpringerLink Account Menu Find a journal Publish with us Search Cart 1.Home …

We consider a model of weakly interacting close-packed dimers on the two-dimensional
square lattice. In a previous paper, we computed both the multi-point dimer correlations …

Consider a surface Ω with a boundary obtained by gluing together a finite number of
equilateral triangles, or squares, along their boundaries, equipped with a vector bundle with …

We use the periodic Schur process, introduced in (Borodin in Duke Math J 140 (3): 391–468
2007), to study the random height function of lozenge tilings (equivalently, dimers) on an …

For Π⊂ R2, a connected, open, bounded set whose boundary is a finite union of disjoint
polygons whose vertices have integer coordinates, the logarithm of the discrete Laplacian …

2.3. Existence of a Kasteleyn weighting 9 2.4. Counting perfect matchings in the bipartite,
non-planar case: periodic boundary conditions 11 2.5. Counting perfect matchings: The …

We study the asymptotic expansion of the determinant of the graph Laplacian associated to
discretizations of a tileable surface endowed with a flat unitary vector bundle. By doing so …