相关论文: Continuity properties of the lower spectral radius

In this article we study a small random perturbation of a linear recurrence equation. If all the roots of its corresponding characteristic equation have modulus strictly less than one, the random linear recurrence goes exponentially fast to…

Spectral rendering accurately reproduces wavelength-dependent appearance but is computationally expensive, as shading must be evaluated at many wavelength samples and scales roughly linearly with the number of samples. It also requires…

We study some spectral properties of a matrix that is constructed as a combination of a Laplacian and an adjacency matrix of simple graphs. The matrix considered depends on a positive parameter, as such we consider the implications in…

A model describing cell membranes as optimal shapes with regard to the $L^2$-deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is shown that the corresponding energy functional is lower…

This paper is concerned with a rate-distortion theory for sequences of i.i.d. random variables with general distribution supported on general sets including manifolds and fractal sets. Manifold structures are prevalent in data science,…

This paper is concerned with regular approximations of spectra of singular discrete linear Hamiltonian systems with one singular endpoint. For any given self-adjoint subspace extension (SSE) of the corresponding minimal subspace, its…

Given a family of self-adjoint operators $(A_t)_{t\in T}$ indexed by a parameter $t$ in some topological space $T$, necessary and sufficient conditions are given for the spectrum $\sigma(A_t)$ to be Vietoris continuous with respect to $t$.…

For the almost Mathieu operator with a small coupling constant, for a series of spectral gaps, we describe the asymptotic locations of the gaps and get lower bounds for their lengths. The results are obtained by analysing a monodromy…

We study spectral properties of quantum radiation of ultimately short duration. In particular, we introduce a continuous multimode squeezing operator for the description of subcycle pulses of entangled photons generated by a coherent-field…

The high-frequency integrated spectra of Compact Steep Spectrum (CSS) sources show breaks with a moderate spectral steepening well fitted by continuous injection synchrotron spectra. In lobe-dominated CSS sources the radiative ages deduced…

We study models where the superpartners of the ordinary particles have continuous spectra rather than being discrete states, which can occur when the supersymmetric standard model is coupled to an approximately conformal sector. We show…

Our theory relates the secondary spectrum, the 2D power spectrum of the radio dynamic spectrum, to the scattered pulsar image in a thin scattering screen geometry. Recently discovered parabolic arcs in secondary spectra are generic features…

New insights into transport properties of nanostructures with a linear dispersion along one direction and a quadratic dispersion along another are obtained by analysing their spectral stability properties under small perturbations.…

Consider a truncated circular unitary matrix which is a $p_n$ by $p_n$ submatrix of an $n$ by $n$ circular unitary matrix by deleting the last $n-p_n$ columns and rows. Jiang and Qi (2017) proved that the maximum absolute value of the…

The open problem of calculating the limiting spectrum (or its Shannon transform) of increasingly large random Hermitian finite-band matrices is described. In general, these matrices include a finite number of non-zero diagonals around their…

The geometric Langlands program is distinguished in assigning spectral decompositions to all representations, not only the irreducible ones. However, it is not even clear what is meant by a spectral decomposition when one works with…

We study the spectrum of 4-cycle row-stochastic matrices. For real eigenvalues the spectral region is [-1,1]. For nonreal eigenvalues a+ib we derive necessary conditions in terms of the real and imaginary parts, including the inequality…

The anomalous excess of small-kT photons radiated along with multi-hadron production, is challenging the physics community over four decades, but no solution has been proposed so far. We argue that the problem is rooted in the comparison…

We give an effective bound of the joint spectral radius $\rho(\Sigma)$ for a finite set $\Sigma$ of nonnegative matrices: For every $n$, \[ \sqrt[n]{\left(\frac{V}{UD}\right)^{D} \max_C \max_{i,j\in C} \max_{A_1,\dots,A_n\in\Sigma}(A_1\dots…

We study linear cocycles generated by nonautonomous delay equations in a suitable Hilbert space and their extensions, called compound cocycles, to exterior powers. Using a recent version of the frequency theorem, we develop analytical…