相关论文: The joint translation spectrum and Manhattan manif…

We introduce the notion of \emph{joint spectrum} of a compact set of matrices $S \subset GL_d(\mathbb{C})$, which is a multi-dimensional generalization of the joint spectral radius. We begin with a thorough study of its properties (under…

Recently, several research efforts showed that the analysis of joint spectral characteristics of sets of matrices is greatly eased when these matrices share an invariant cone. In this short note we prove two new results in this direction.…

We introduce a new method for studying length spectrum rigidity problems based on a combination of ideas from dynamical systems and geometric group theory. This allows us to compare the marked length spectrum of metrics and distance-like…

This article represents a major step in the unification of the theory of algebraic, topological and singular transition matrices by introducing a definition which is a generalization that encompasses all of the previous three. When this…

We define a family of four-point invariants for Shilov boundaries of bounded symmetric domains of tube type, which generalizes the classical four-point cross ratio on the unit circle. This generalization, which is based on a similar…

Let $Z$ be a projective hypersurface such that its underlying reduced variety has only isolated singularities. In case its irreducible components have constant multiplicities, for instance if $\dim Z>1$, we show that the spectrum of its…

We obtain sequences of inclusion sets for the spectrum, essential spectrum, and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. Each inclusion set is the union of the pseudospectra of certain…

In this paper, we study the asymptotic translation lengths on the sphere complexes of monodromies of a manifold fibered over the circle. Given a compact mapping torus, we define a cone in the first cohomology which we call the generalized…

Measurement-induced phase transitions (MIPTs) are known to be described by non-unitary conformal field theories (CFTs) whose precise nature remains unknown. Most physical quantities of interest, such as the entanglement features of quantum…

We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- which share a common subset of nodes, and propose a method for…

We consider a network model, embedded on the Manhattan lattice, of a quantum localisation problem belonging to symmetry class C. This arises in the context of quasiparticle dynamics in disordered spin-singlet superconductors which are…

We study the spectral properties of the transfer matrix for a gonihedric random surface model on a three-dimensional lattice. The transfer matrix is indexed by generalized loops in a natural fashion and is invariant under a group of motions…

Implementing an idea due to John Baez and James Dolan we define new invariants of Whitney stratified manifolds by considering the homotopy theory of smooth transversal maps. To each Whitney stratified manifold we assign transversal homotopy…

We consider random walk on a mildly random environment on finite transitive d- regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An…

Joint spectral embeddings facilitate analysis of multiple network data by simultaneously mapping vertices in each network to points in Euclidean space where statistical inference is then performed. In this work, we consider one such joint…

We study spectral and transport properties of one-dimensional tight-binding $\mathcal{PT}$-symmetric chains with alternating couplings. Based on the transfer matrix method, we have analytically developed the expressions for the transmission…

We study the spectrum of the join of several circulant matrices. We apply our results to compute explicitly the spectrum of certain graphs obtained by joining several circulant graphs.

Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a…

We prove several results about the relationship between the word complexity function of a subshift and the set of Turing degrees of points of the subshift, which we call the Turing spectrum. Among other results, we show that a Turing…

This manuscript introduces a new framework for the study of knots by exploring the neighborhood of knot embeddings in the space of simple open and closed curves in 3-space. The latter gives rise to a knotoid spectrum, which determines the…