1,382 research outputs found
Free Stein kernels and an improvement of the free logarithmic Sobolev inequality
We introduce a free version of the Stein kernel, relative to a semicircular
law. We use it to obtain a free counterpart of the HSI inequality of Ledoux,
Peccatti and Nourdin, which is an improvement of the free logarithmic Sobolev
inequality of Biane and Speicher, as well as a rate of convergence in the
(multivariate) entropic free Central Limit Theorem. We also compute the free
Stein kernels for several relevant families of self-adjoint operators
Free monotone transport for infinite variables
We extend the free monotone transport theorem of Guionnet and Shlyakhtenko to
the case of infinite variables. As a first application, we provide a criterion
for when mixed -Gaussian algebras are isomorphic to ;
namely, when the structure array of a mixed -Gaussian algebra has
uniformly small entries that decay sufficiently rapidly. Here a mixed
-Gaussian algebra with structure array is
the von Neumann algebra generated by and
are the Fock space representations of the commutation relation
,
- β¦