5 papers
On aggregation-quantization permutability problem for discrete-time Markov chains
Adam Doliwa, Artur Siemaszko, Adam Zalewski
Given random walk on a graph, the corresponding discrete-time quantum walk can be constructed using the method proposed by Szegedy. On the other hand, given a partition of the set…
Non-commutative multiple bi-orthogonal polynomials: formal approach and integrability
Adam Doliwa
We define the non-commutative multiple bi-orthogonal polynomial systems, which simultaneously generalize the concepts of multiple orthogonality, matrix orthogonal polynomials and o…
Determinantal approach to multiple orthogonal polynomials, and the corresponding integrable equations
Adam Doliwa
We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Padé ap…
Hermite-Padé approximation, multiple orthogonal polynomials, and multidimensional Toda equations
Adam Doliwa
We review recent results on the connection between Hermite-Padé approximation problem, multiple orthogonal polynomials, and multidimensional Toda equations in continuous and discre…
Spectral quantization of discrete random walks on half-line, and orthogonal polynomials on the unit circle
Adam Doliwa, Artur Siemaszko
We define quantization scheme for discrete-time random walks on the half-line consistent with Szegedy's quantization of finite Markov chains. Motivated by the Karlin and McGregor d…