3 papers
quant-ph2026
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…
nlin.SI2025
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…
math-ph2024
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…