18 citations · 78 across the 23 of their papers we have counts for
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Infinitesimal moments in free and c-free probability and Motzkin paths
Romuald Lenczewski
Infinitesimal moments associated with infinitesimal freeness and infinitesimal conditional freeness are studied. For free random variables, we consider continuous deformations of m…
Decomposition of free cumulants
Romuald Lenczewski
Free cumulants are multilinear functionals defined in terms of the moment functional with the use of the family of lattices of noncrossing partitions. In the univariate case, they…
Motzkin path decompositions of functionals in noncommutative probability
Romuald Lenczewski
We study the decomposition of free random variables in terms of their orthogonal replicas from a new perspective. First, we show that the mixed moments of orthogonal replicas with…
Conditionally monotone independence and the associated products of graphs
Romuald Lenczewski
We reduce the conditionally monotone (c-monotone) independence of Hasebe to tensor independence. For that purpose, we use the approach developed for the reduction of boolean, free…
Random matrices, continuous circular systems and the triangular operator
Romuald Lenczewski
We present a Hilbert space approach to the limit joint *-distributions of complex independent Gaussian random matrices. For that purpose, we use a suitably defined family of creati…
Limit distributions of Gaussian block ensembles
Romuald Lenczewski
It has been shown by Voiculescu that important classes of square independent random matrices are asymptotically free, where freeness is a noncommutative analog of classical indepen…