We consider Schrödinger operators on the real line with limitperiodic potentials and show that, generically, the spectrum is a Cantor set of zero Lebesgue measure and all spectral measures are purely singular continuous. Moreover, we show that for a dense set of limit-periodic potentials, the spectrum of the associated Schrödinger operator has Hausdorff dimension zero. In both results one can i...

It is known that, for site percolation on the Cayley graph of a cocompact Fuchsian group of genus ≥ 2, infinitely many infinite connected clusters exist almost surely for certain values of the parameter p = P{site is open}. In such cases, the set Λ of limit points at ∞ of an infinite cluster is a perfect, nowhere dense set of Lebesgue measure 0. In this paper, a variational formula for the Haus...

Using the domain-theoretic model for geometric computation, we define the partial Delaunay triangulation and the partial Voronoi diagram of N partial points in R2 and show that these operations are domain-theoretically computable and effectively computable with respect to Hausdorff distance and Lebesgue measure. These results are obtained by showing that the map which sends three partial points...

The generator matrices of polar codes and ReedMuller codes are submatrices of a Kronecker product of a lower-triangular binary square matrix. These submatrices are chosen according to an index set pointing to rows, which for polar codes minimize the Bhattacharyya parameter, and which for Reed-Muller codes maximize the Hamming weight. This work investigates the properties of this index set in th...