133 citations · 795 across the 60 of their papers we have counts for
69 papers
Emergence in graphs with near-extreme constraints
Charles Radin, Lorenzo Sadun
We consider entropy-optimal graphons associated with extreme and near-extreme constraints on the densities of edges and triangles. We prove that the optimizers for near-extreme con…
How big is a tiling's return module?
Abigail Perryman, Lorenzo Sadun
The rank of a tiling's return module depends on the geometry of its tiles and is not a topological invariant. However, the rank of the first \v Cech cohomology give…
Dynamics and topology of the Hat family of tilings
Michael Baake, Franz Gähler, Lorenzo Sadun
The recently discovered Hat tiling admits a 4-dimensional family of shape deformations, including the 1-parameter family already known to yield alternate monotiles. The continuous…
Optimal graphons in the edge-2star model
Charles Radin, Lorenzo Sadun
In the edge-2star model with hard constraints we prove the existence of an open set of constraint parameters, bisected by a line segment on which there are nonunique entropy-optima…
Existence of a symmetric bipodal phase in the edge-triangle model
Joe Neeman, Charles Radin, Lorenzo Sadun
In the edge-triangle model with edge density close to 1/2 and triangle density below 1/8 we prove that the unique entropy-maximizing graphon is symmetric bipodal. We also prove tha…
Typical large graphs with given edge and triangle densities
Joe Neeman, Charles Radin, Lorenzo Sadun
The analysis of large simple graphs with extreme values of the densities of edges and triangles has been extended to the statistical structure of typical graphs of fixed intermedia…