We establish several methods for constructing stationary self-similar random elds (ssf ’s) on the integer lattice by “random wavelet expansion”, which stands for representation of random elds by sums of randomly scaled and translated functions, or more generally, by composites of random functionals and deterministic wavelet expansion. To construct ssf ’s on the integer lattice, random wavelet e...

Simulating fermionic lattice models with qubits requires mapping fermionic degrees of freedom to qubits. The simplest method for this task, the Jordan-Wigner transformation, yields strings of Pauli operators acting on an extensive number of qubits. This overhead can be a hindrance to implementation of qubit-based quantum simulators, especially in the analog context. Here we thus review and anal...

We study how the existence in an algebraic lattice L of a chain of a given type is reflected in the join-semilattice K(L) of its compact elements. We show that for every chain α of size κ, there is a set B of at most 2 join-semilattices, each one having a least element such that an algebraic lattice L contains no chain of order type I(α) if and only if the join-semilattice K(L) of its compact e...

As an invited speaker of the ACISP 2017 conference, Dongxi Liu recently introduced a new lattice-based encryption scheme (joint work with Li, Kim and Nepal) designed for lightweight IoT applications, and announced plans to submit it to the NIST postquantum competition. The new scheme is based on a variant of standard LWE called Compact-LWE, but is claimed to achieve high security levels in cons...

In this text we are interested in spectral properties of discrete Laplace operators deened on lattices based on nitely-ramiied self-similar sets. The basic example is the lattice based on the Sierpinski gasket. We introduce a new renormalization map which appears to be a rational self-map of a compact complex manifolds. We relate some characteristics of its dynamics with some characteristics of...

We provide some conditions as to when K(X) = K(Y) for two locally compact spaces X and Y (where K(X) is the lattice of all Hausdorr compactiications of X). More speciically, we prove that K(X) = K(Y) if and only if C (X)=C 0 (X) = C (Y)=C 0 (Y). Using this result, we prove several extensions to the case where K(X) is embedded as a sub-lattice of K(Y) and to where X and Y are not locally compact...

In this paper we continue our study of lattices in the automorphisms groups of products of trees initiated in [BM97], [BM00a], [BM00b], [Moz98] (see also [Gla03], [BG02], [Rat04]). We concentrate here on the interplay between the linear representation theory and the structure of these lattices. Before turning to the main results of this paper it may be worthwhile to put certain concepts and res...

We characterize well-founded algebraic lattices by means of forbidden subsemilattices of the join-semilattice made of their compact elements. More specifically, we show that an algebraic lattice L is well-founded if and only if K(L), the join-semilattice of compact elements of L, is well-founded and contains neither [ω], nor Ω(ω∗) as a join-subsemilattice. As an immediate corollary, we get that...

We prove that the interval topology of an Archimedean atomic lattice effect algebra E is Hausdorff whenever the set of all atoms of E is almost orthogonal. In such a case E is order continuous. If moreover E is complete then order convergence of nets of elements of E is topological and hence it coincides with convergence in the order topology and this topology is compact Hausdorff compatible wi...

In 1980 Creutz [1] displayed quark confinement at moderate coupling in lattice simulations of both abelian and nonabelian gauge theories. Whether nonabelian confinement is as much an artifact of Wilson’s action as is abelian confinement remains unclear. The basic variables of Wilson’s formulation [2] are elements of a compact group and enter the action only through traces of their products. The...