The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
We state and prove a noncommutative limit theorem for correlations which are homogeneous with respect to order-preserving injections. The most interesting examples of central limit theorems in quantum probability (for commuting, anticommuting, and free independence and also various q-qclt's), as well as the limit theorems for the Poisson law and the free Poisson law are special cases of the theorem. In particular, the theorem contains the q-central limit theorem for non-identically distributed variables,...
We introduce noncommutative extensions of the Fourier transform of probability measures and its logarithm to the algebra (S) of complex-valued functions on the free semigroup S = FS(z,w) on two generators. First, to given probability measures μ, ν with all moments finite, we associate states μ̂, ν̂ on the unital free *-bialgebra (ℬ,ε,Δ) on two self-adjoint generators X,X’ and a projection P. Then we introduce and study cumulants which are additive under the convolution μ̂* ν̂ = μ̂ ⊗ ν̂ ∘ Δ when...
Download Results (CSV)