46 citations · 498 across the 29 of their papers we have counts for
5 papers · 1 filter
Area limit laws for symmetry classes of staircase polygons
Christoph Richard, Uwe Schwerdtfeger, Bhalchandra Thatte
We derive area limit laws for the various symmetry classes of staircase polygons on the square lattice, in a uniform ensemble where, for fixed perimeter, each polygon occurs with t…
Random colourings of aperiodic graphs: Ergodic and spectral properties
Peter Müller, Christoph Richard
We study randomly coloured graphs embedded into Euclidean space, whose vertex sets are infinite, uniformly discrete subsets of finite local complexity. We construct the appropriate…
Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies
Michael Baake, Daniel Lenz, Christoph Richard
Delone sets of finite local complexity in Euclidean space are investigated. We show that such a set has patch counting and topological entropy 0 if it has uniform cluster frequenci…
Limit distributions and scaling functions
Christoph Richard
We discuss the asymptotic behaviour of models of lattice polygons, mainly on the square lattice. In particular, we focus on limiting area laws in the uniform perimeter ensemble whe…
Area distribution and scaling function for punctured polygons
Christoph Richard, Iwan Jensen, Anthony J. Guttmann
Punctured polygons are polygons with internal holes which are also polygons. The external and internal polygons are of the same type, and they are mutually as well as self-avoiding…