Otros Seminarios

Banded Hessenberg operators, multiple orthogonal polynomials and random walks

Ponente:  Ana Foulquie-Moreno, Universidade de Aveiro; y Amílcar Branquinho, Universidade de Coimbra ()
Fecha:  viernes 15 de julio de 2022 - 11:00
Lugar:  Aula Naranja, ICMAT


The large knowledge on the spectral and factorization properties of oscillatory and totally nonnegative matrices leads to a spectral Favard theorem for the class of the so called regular oscillatory banded Hessenberg matrices, so that bidiagonal positive factorization holds, in terms of sequences of multiple orthogonal polynomials of types II and I with respect to a set of positive Lebesgue-Stieltjes measures. 

The spectral Favard theorem is then applied to Markov chains with tetradiagonal transition matrices, i.e. beyond birth and death. In the finite case, the Karlin-McGregor spectral representation is given, it is shown that the random walks are recurrent and explicit expressions in terms of the orthogonal polynomials for the stationary distributions are given. Similar results are obtained for the countable infinite Markov chain.

This is a joint work with Manuel Mañas, University Complutense of Madrid & ICMAT.