Related papers: System bandwidth and the existence of generalized …
We provide an ergodic theorem for certain Banach-space valued functions on structures over $\ZZ^d$, which allow for existence of frequencies of finite patterns. As an application we obtain existence of the integrated density of states for…
In the restricted setting of product phase space lattices, we give an alternate proof of P. Linnell's theorem on the finite linear independence of lattice Gabor systems in $L^2(\mathbb R^d)$. Our proof is based on a simple argument from the…
We prove mean and pointwise ergodic theorems for general families of averages on a semisimple algebraic (or S-algebraic) group G, together with an explicit rate of convergence when the action has a spectral gap. Given any lattice in G, we…
This work addresses the question of achieving capacity with lattice codes in multi-antenna block fading channels when the number of fading blocks tends to infinity. A design criterion based on the normalized minimum determinant is proposed…
Suppose $G$ is an amenable locally compact group. If $\{F_\gamma\} = \{F_\gamma\}_{\gamma\in\Gamma}$ is a F\o{}lner net for $G$, associate it with the net $\{\chi_{F_\gamma} / |F_\gamma|\} \subset L_1(G) \subset L_\infty^*(G)$. Thus, every…
We give a general construction of entire functions in $d$ complex variables that vanish on a lattice of the form $L = A (Z + i Z )^d$ for an invertible complex-valued matrix. As an application we exhibit a class of lattices of density >1…
Recent years have seen the concept of global symmetry extended to non-invertible (or categorical) symmetries, for which composition of symmetry generators is not necessarily invertible. Such non-invertible symmetries lead to a…
We use finite group topological lattice gauge theory, also known as the quantum double model, as a lens to explore a notion of topological order enriched by a non-invertible symmetry. For invertible symmetry enriched topological order,…
We consider stochastic dynamics of lattice systems with finite local state space, possibly at low temperature, and possibly non-reversible. We assume the additional regularity properties on the dynamics: a) There is at least one stationary…
The statistics of particles and extended excitations, such as loops and membranes, are fundamental to modern condensed matter physics, high-energy physics, and quantum information science, yet a comprehensive lattice-level framework for…
Given a lattice $\Lambda$ in a locally compact abelian group $G$ and a measurable subset $\Omega$ with finite and positive measure, then the set of characters associated to the dual lattice form a frame for $L^2(\Omega)$ if and only if the…
Consideration of the asteroid belt (Kuiper belt) as a jammed-granular media establishes a bridge between condensed matter physics and astrophysics. It opens up an experimental possibility to determine the deformation parameters for…
We introduce the space of infinite volume ends of a locally compact second countable (lcsc) space that admits a Radon measure. In certain cases, this coincides with the classical space of ends. Consider a discrete subgroup $\Gamma$ of a…
We obtain a compactness result for $\Gamma$-convergence of integral functionals defined on $\mathcal{A}$-free vector fields. This is used to study homogenization problems for these functionals without periodicity assumptions. More…
We show the full structure of the frame set for the Gabor system $\mathcal{G}(g;\alpha,\beta):=\{e^{-2\pi i m\beta\cdot}g(\cdot-n\alpha):m,n\in\Bbb Z\}$ with the window being the Haar function $g=-\chi_{[-1/2,0)}+\chi_{[0,1/2)}$. The…
Anomaly matching for continuous symmetries has been the primary tool for establishing symmetry enforced gaplessness - the phenomenon where global symmetry alone forces a quantum system to be gapless in the infrared. We introduce a new…
We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…
We analyze a class of mean-field (MF) lattice-fermion Hamiltonians and construct the corresponding grand-canonical density operator for such system. New terms are introduced, which may be interpreted as local fugacities, molecular fields,…
Let G be a stratified Lie group and L be the sub-Laplacian on G. Let 0 \neq f\in S(R^+). We show that Lf(L)\delta, the distribution kernel of the operator Lf(L), is an admissible function on G. We also show that, if \xi f(\xi) satisfies…
Wave motion in a continuous elastic rod with a periodically attached inertial-amplification mechanism is investigated. The mechanism has properties similar to an "inerter" typically used in vehicle suspensions, however here it is…