Matrix Liberation Process II: Relation to Orbital Free Entropy

Orbital Approach to Microstate Free Entropy

Motivated by Voiculescu’s liberation theory, we introduce the orbital free entropy χorb for non-commutative self-adjoint random variables (also for “hyperfinite random multivariables”). Besides its basic properties the relation of χorb with the usual free entropy χ is shown. Moreover, the dimension counterpart of χorb is discussed.

Inequalities Related to Free Entropy Derived from Random Matrix Approximation

Biane proved the free analog of the logarithmic Sobolev inequality for probability measures on R by means of random matrix approximation procedure. We show that the same method can be applied to reprove Biane and Voiculescu’s free analog of Talagrand’s transportation cost inequality for measures on R. Furthermore, we prove the free analogs of the logarithmic Sobolev inequality and the transport...

The Relation of the Spinal Cord to the Spontaneous Liberation

I want to break free: liberation from noninvasive ventilation.

A lot of emphasis has been placed on the weaning process from invasive mechanical ventilation, since prolonged ventilation has been associated with increased length of intensive care unit stay, increased levels of complications and increased costs. Weaning in this respect may be considered as an “all or none” phenomenon, since the patients are abruptly removed from any form of ventilator suppor...

B DuBois and the Process of Liberation

In one of the essays, ‘The American Experience of B R Ambedkar’ included in her book, From Untouchable to Dalit, Eleanor Zelliot writes: “A direct comparison between the Negroes of America and Untouchables of India does not appear in Ambedkar’s writings.” She may be right, in a way, but Ambedkar does make comparison between slaves and untouchables, cites parallel cases and also shows how Hindus...