Related papers: Spectral analysis of bilateral birth-death process…
The statistical distribution of eigenvalues of pairs of coupled random matrices can be expressed in terms of integral kernels having a generalized Christoffel--Darboux form constructed from sequences of biorthogonal polynomials. For…
An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex…
By considering an empirical approximation, and a new class of operators that we will call walking operators, we construct, for any positive ND-toeplitz matrix, an infinite in all dimensions matrix, for which the inverse approximates the…
A probability measure in R^d is called a spectral measure if it has an orthonormal basis consisting of exponentials. In this paper we study spectral Cantor measures. We establish a large class of such measures and give a necessary and…
In many applications it is important to understand the sensitivity of eigenvalues of a matrix polynomial to perturbations of the polynomial. The sensitivity commonly is described by condition numbers or pseudospectra. However, the…
The spectral representation is an effecient tool to explore electrical properties of material mixtures. It separates the contributions of geometrical topology and intrinsic properties of the constituents in the system. The aim of this paper…
We give a very brief introduction to the machinery of spectral sequences, including the spectral sequence of a bicomplex. We then briefly introduce a generalisation of the spectral sequences of a bicomplex to the spectral sequences of…
We study the spectrum of single-photon emission and scattering in a mixed optomechanical model which consists of both linear and quadratic optomechanical interactions. The spectra are calculated based on the exact long-time solutions of the…
Repetitions within a given genealogical tree provides some information about the degree of consanguineity of a population. They can be analyzed with techniques usually employed in statistical physics when dealing with fixed point…
The first paper in this series introduced a new family of nonasymptotic matrix concentration inequalities that sharply capture the spectral properties of very general random matrices in terms of an associated noncommutative model. These…
This handbook chapter gives a modern introduction to spectral analysis of celestial X-ray sources. Concepts presented include the instrumentation response, the linear modelling approximation, Poisson count statistics and the Gaussian…
Two-dimensional spectroscopy is discussed for open quantum systems with multiple simultaneously measurable fluxes. In particular, we discuss a junction where optical measurements of photon flux are complemented with simultaneous transport…
This is a review paper outlining recent progress in the spectral analysis of first order systems. We work on a closed manifold and study an elliptic self-adjoint first order system of linear partial differential equations. The aim is to…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
First, we revisit the stochastic Luria-Delbr\"uck model: a classic two-type branching process which describes cell proliferation and mutation. We prove limit theorems and exact results for the mutation times, clone sizes, and number of…
In this paper we introduce a model which provides a new approach to the phenomenon of stochastic resonance. It is based on the study of the properties of the stationary distribution of the underlying stochastic process. We derive the…
Many spatio-temporal data record the time of birth and death of individuals, along with their spatial trajectories during their lifetime, whether through continuous-time observations or discrete-time observations. Natural applications…
Condition numbers of random polynomial systems have been widely studied in the literature under certain coefficient ensembles of invariant type. In this note we introduce a method that allows us to study these numbers for a broad family of…