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We consider a finite family of invertible $2 \times 2$ real matrices and a transitive Markov shift on the index set. Let $\lambda$ be the top Lyapunov exponent for random matrix products driven by the Markov shift. We prove that, if the…
We present a detailed study of the scattering system given by the Neumann Laplacian on the discrete half-space perturbed by a periodic potential at the boundary. We derive asymptotic resolvent expansions at thresholds and eigenvalues, we…
The optimum interval method for finding an upper limit of a one-dimensionally distributed signal in the presence of an unknown background is extended to the case of high statistics. There is also some discussion of how the method can be…
We provide the first known upper bounds for the packing dimension of weighted singular and weighted $\omega$-singular matrices. We also prove upper bounds for these sets when intersected with fractal subsets. The latter results, even in the…
We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state…
We prove bounds on the minimal time for quantum messaging, propagation/creation of correlations, and control of states for general lattice quantum many-body systems. The proofs are based on a maximal velocity bound, which states that the…
We investigate the quantitative relationship between operator spreading and classical information propagation in quantum systems. Focusing on a bi-partite quantum channel, we derive new upper and lower bounds on the Holevo capacity, a…
We study the double scaling limit for unitary invariant ensembles of random matrices with non analytic potentials and find the asymptotic expansion for the entries of the corresponding Jacobi matrix. Our approach is based on the…
We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
A sequence of invertible matrices given by a small random perturbation around a fixed diagonal partially hyperbolic matrix induces a random dynamics on the Grassmann manifolds. Under suitable weak conditions it is known to have a unique…
We develop a powerful and general method to provide rigorous and accurate upper and lower bounds for Lyapunov exponents of stochastic flows. Our approach is based on computer-assisted tools, the adjoint method and established results on the…
We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…
Using a density matrix description in space we study the evolution of wavepackets in a fluctuating space-time background. We assume that space-time fluctuations manifest as classical fluctuations of the metric. From the non-relativistic…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
As shown in Phys. Rev. A 96, 020101(R) (2017), it is possible to demonstrate that quantum particles do not move along straight lines in free space by increasing the probability of finding the particles within narrow intervals of position…
An effective operational approach to quantum mechanics is to focus on the evolution of wave-packets, for which the wave-function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of…
Covering arrays find important application in software and hardware interaction testing. For practical applications it is useful to determine or bound the minimum number of rows, CAN$(t,k,v)$, in a covering array for given values of the…
In this paper, we extend and complement previous works about propagation in kinetic reaction-transport equations. The model we study describes particles moving according to a velocity-jump process, and proliferating according to a reaction…
We describe a suite of fast algorithms for evaluating Jacobi polynomials, applying the corresponding discrete Sturm-Liouville eigentransforms and calculating Gauss-Jacobi quadrature rules. Our approach is based on the well-known fact that…