Related papers: Spectral analysis of bilateral birth-death process…
In this paper we study explicit strong solutions for two difference-differential fractional equations, defined via the generator of an immigration-death process, by using spectral methods. Moreover, we give a stochastic representation of…
We study the analytic structure of partial-wave amplitudes derived from u- and t-channel exchange processes. The latter plays a crucial role in dispersion-theory approaches to coupled-channel systems that model final state interactions in…
Line-by-line calculations are becoming the standard procedure for carrying spectral simulations. However, it is important to insure the accuracy of such spectral simulations through the choice of adapted models for the simulation of key…
A new derivation method of duality relations in stochastic processes is proposed. The current focus is on the duality between stochastic differential equations and birth-death processes. Although previous derivation methods have been based…
This paper defines the multivariate Krawtchouk polynomials, orthogonal on the multinomial distribution, and summarizes their properties as a review. The multivariate Krawtchouk polynomials are symmetric functions of orthogonal sets of…
The simple (linear) birth-and-death process is a widely used stochastic model for describing the dynamics of a population. When the process is observed discretely over time, despite the large amount of literature on the subject, little is…
This paper aims to clarify certain aspects of the relations between birth-death processes, measures solving a Stieltjes moment problem, and sets of parameters defining polynomial sequences that are orthogonal with respect to such a measure.…
The aim of this paper is to describe a population model with transition. We analyze the spectral properties of the transition matrix considering both irreducible and reducible structures. We give physical interpretations of these properties…
We study large deviation properties of random matricial spectral measures.
For a large class of integral operators or second order differential operators, their isospectral (or cospectral) operators are constructed explicitly in terms of $h$-transform (duality). This provides us a simple way to extend the known…
As widely known, the basic reproduction number plays a key role in weighing birth/infection and death/recovery processes in several models of population dynamics. In this general setting, its characterization as the spectral radius of next…
In this review, we discuss the applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principles of the theory of these processes are briefly described.…
In this article, we consider two proper double splittings satisfying certain conditions, of a semi-monotone rectangular matrix A and derive new comparison results for the spectral radii of the correspond ing iteration matrices. These…
We present an analytic method for calculating spectral densities of empirical covariance matrices for correlated data. In this approach the data is represented as a rectangular random matrix whose columns correspond to sampled states of the…
We consider a bilateral birth-death process characterized by a constant transition rate $\lambda$ from even states and a possibly different transition rate $\mu$ from odd states. We determine the probability generating functions of the even…
We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to those predicted by suitable random matrix theory ensembles,…
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…
We present an unified framework to identify spectra of Jacobi matrices. We give applications to long-standing conjecture of Chihara concerning one-quarter class of orthogonal polynomials, to the conjecture posed by Roehner and Valent…
We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the…
In these notes we review recent progress (and, in Section \ref{sec:ados}, we announce a new result) concerning the statistical properties of the spectrum of Wigner random matrices.