Approximation of Quantum L ´ Evy Processes by Quantum Random Walks

@inproceedings{Skalski2007ApproximationOQ,
title={Approximation of Quantum L ´ Evy Processes by Quantum Random Walks},
author={Adam G. Skalski},
year={2007}
}

Every quantum Lévy process with a bounded stochastic generator is shown to arise as a strong limit of a family of suitably scaled quantum random walks. The note is concerned with investigating convergence of random walks on quantum groups to quantum Lévy processes. The theory of the latter is a natural non-commutative counterpart of the theory of classical Lévy processes on groups ([Hey]). It has been initiated in [ASW] and further extensively developed by Schürmann, Schott and the first named… CONTINUE READING