Zobrazeno 1 - 10
of 119
pro vyhledávání: '"De la Iglesia, Manuel D."'
Publikováno v:
J. Phys. A: Math. Theor. 57 (2024) 295301 (33pp)
Quantum Markov chains (QMCs) are positive maps on a trace-class space describing open quantum dynamics on graphs. Such objects have a statistical resemblance with classical random walks, while at the same time it allows for internal (quantum) degrees
Externí odkaz:
http://arxiv.org/abs/2402.15878
We give a probabilistic interpretation of the associated Jacobi polynomials, which can be constructed from the three-term recurrence relation for the classical Jacobi polynomials by shifting the integer index $n$ by a real number $t$. Under certain r
Externí odkaz:
http://arxiv.org/abs/2301.07582
We study a family of quasi-birth-and-death (QBD) processes associated with the so-called first family of Jacobi-Koornwinder bivariate polynomials. These polynomials are orthogonal on a bounded region typically known as the swallow tail. We will expli
Externí odkaz:
http://arxiv.org/abs/2212.05041
We consider discrete-time birth-death chains on a spider, i.e. a graph consisting of $N$ discrete half lines on the plane that are joined at the origin. This process can be identified with a discrete-time quasi-birth-death process on the state space
Externí odkaz:
http://arxiv.org/abs/2111.10450
Publikováno v:
Quantum Information Processing 22:60 (2023)
Inspired by the classical spectral analysis of birth-death chains using orthogonal polynomials, we study an analogous set of constructions in the context of open quantum dynamics and related walks. In such setting, block tridiagonal matrices and matr
Externí odkaz:
http://arxiv.org/abs/2107.10214
Autor:
de la Iglesia, Manuel D.
We consider the spectral analysis of several examples of bilateral birth-death processes and compute explicitly the spectral matrix and the corresponding orthogonal polynomials. We also use the spectral representation to study some probabilistic prop
Externí odkaz:
http://arxiv.org/abs/2105.14419
The list of physically motivated urn models that can be solved in terms of classical orthogonal polynomials is very small. It includes a model proposed by D. Bernoulli and further analyzed by S. Laplace and a model proposed by P. and T. Ehrenfest and
Externí odkaz:
http://arxiv.org/abs/2105.00614
We study the bispectrality of Jacobi type polynomials, which are eigenfunctions of higher-order differential operators and can be defined by taking suitable linear combinations of a fixed number of consecutive Jacobi polynomials. Jacobi type polynomi
Externí odkaz:
http://arxiv.org/abs/2012.07618
We consider a new way of factorizing the transition probability matrix of a discrete-time birth-death chain on the integers by means of an absorbing and a reflecting birth-death chain to the state 0 and viceversa. First we will consider reflecting-ab
Externí odkaz:
http://arxiv.org/abs/2011.13343
The aim of this paper is to study some models of quasi-birth-and-death (QBD) processes arising from the theory of bivariate orthogonal polynomials. First we will see how to perform the spectral analysis in the general setting as well as to obtain res
Externí odkaz:
http://arxiv.org/abs/2002.04536