Brent Nelson

On Two-faced Families of Non-commutative Random Variables

We demonstrate that the notions of bi-free independence and combinatorial-bi-free independence of two-faced families are equivalent using a diagrammatic view of bi-non-crossing partitions. These diagrams produce an operator model on a Fock space suitable for representing any two-faced family of non-commutative random variables. Furthermore, using a Kreweras complement on bi-non-crossing partitions we establish the expected formulas for the multiplicative convolution of a bi-free pair of two-faced families.

Free Monotone Transport Without a Trace

We adapt the free monotone transport results of Guionnet and Shlyakhtenko to the type III case. As a direct application, we obtain that the q-deformed Araki–Woods algebras are isomorphic (for sufficiently small

Radiative Properties of Polar Bear Hair

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Free transport for finite depth subfactor planar algebras

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An application of free transport to mixed -Gaussian algebras

In this paper, we develop the theory of bi-freeness in an amalgamated setting. We construct the operator-valued bi-free cumulant functions, and show that the vanishing of mixed cumulants is necessary and sufficient for bi-free independence with amalgamation. Further, we develop a multiplicative convolution for operator-valued random variables and explore ways to construct bi-free pairs of B-faces.

Free Monotone Transport for Infinite Variables

The polar bear’s ability to survive in the harsh arctic night fascinates scientific and lay audiences alike, giving rise to anecdotal and semi-factual stories on the radiative properties of the bear’s fur which permeate the popular literature, television programs, and textbooks [1–5]. One of the most interesting radiative properties of polar bear fur is that it is invisible in the infrared region. Some theories have attempted to explain this by claiming that the outer temperature of the fur is the same as that of the environment. However, this explanation is unsatisfactory because surface radiation depends on both the surface temperature and the surface radiative properties [6].Copyright

Free Stein kernels and an improvement of the free logarithmic Sobolev inequality

Abstract In this article, we study a form of free transport for the interpolated free group factors, extending the work of Guionnet and Shlyakhtenko for the usual free group factors [11] . Our model for the interpolated free group factors comes from a canonical finite von Neumann algebra M ( Γ , μ ) associated to a finite, connected, weighted graph ( Γ , V , E , μ ) [12] , [13] . With this model, we use an operator-valued version of Voiculescus free difference quotient introduced in [13] to state a Schwinger–Dyson equation which is valid for the generators of M ( Γ , μ ) . We construct free transport for appropriate perturbations of this equation. Also, M ( Γ , μ ) can be constructed using the machinery of Shlyakhtenkos operator-valued semicircular systems [24] .