Abstract:
In this talk we consider a class of discrete energies on lattices in Euclidean spaces that, to a given finite collection of lattice points, associate an edge-perimeter type functional (whose range goes beyond nearest neighbours). If we increase the number of points considered and shrink down the lattice we show that, in the limit, the functionals converge to a continuum anisotropic perimeter, with a crystalline Wulff shape. With the same techniques we also find Wulff shapes arising in a similar scaled-down limit for a class of perimeter energies defined on quasiperiodic tilings, such as the Penrose tiling. Based on a joint work with Mircea Petrache (Pontificia Universidad Católica de Chile).