18 citations · 78 across the 23 of their papers we have counts for
7 papers · 1 filter
Noncommutative Brownian motions with Kesten distributions and related Poisson processes
Romuald Lenczewski, Rafal Salapata
We introduce and study a noncommutative two-parameter family of noncommutative Brownian motions in the free Fock space. They are associated with Kesten laws and give a continuous i…
Discrete interpolation between monotone probability and free probability
Romuald Lenczewski, Rafal Salapata
We construct a sequence of states called m-monotone product states which give a discrete interpolation between the monotone product of states of Muraki and the free product of stat…
Reduction of free independence to tensor independence
Romuald Lenczewski
We show how to reduce free independence to tensor independence in the strong sense. We construct a suitable unital *-algebra of closed operators `affiliated' with a given unital *-…
Filtered random variables, bialgebras and convolutions
Romuald Lenczewski
We introduce the filtered *-bialgebra which is a noncommutative analog of the *-bialgebra of multivariate polynomials with the canonical coproduct and counit. We study the associat…
Filtered stochastic calculus
Romuald Lenczewski
By introducing a color filtration to the multiplicity space, we extend the quantum Ito calculus on multiple symmetric Fock space to the framework of filtered adapted biprocesses. I…
Limit theorems for the hierarchy of freeness
Uwe Franz, Romuald Lenczewski
The central limit theorem, the invariance principle and the Poisson limit theorem for the hierarchy of freeness are studied. We show that for given natural m the limit laws can be…