Local Functional Inequalities in One Dimensional Free Probability
Ionel Popescu
TL;DR
This paper establishes sharp local and potential-independent inequalities in one-dimensional free probability, extending to the entire real line, with implications for transportation and functional inequalities in free probability theory.
Contribution
It introduces and proves sharp local and potential-independent inequalities in one-dimensional free probability, including a new approach to free transportation inequality on the real line.
Findings
Established sharp local and potential-independent inequalities
Recovered a recent free transportation inequality on the real line
Extended inequalities to compact intervals in free probability
Abstract
In this note we introduce and prove local and potential independent transportation, Log-Sobolev and HWI inequalities in one dimensional free probability on compact intervals which are sharp. We recover using this approach a free transportation inequality on the whole real line which was put forward recently by M. Maida and E. Maurel-Segala.
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